Answer with Explanation:
By definition of acceleration we have
[tex]a=\frac{dv}{dt}[/tex]
Given [tex]a=kv^{2}[/tex], using this value in the above equation we get
[tex]kv^2=\frac{dv}{dt}\\\\\frac{dv}{v^{1}}=kdt[/tex]
Upon integrating on both sides we get
[tex]\int \frac{dv}{v^2}=\int kdt\\\\-\frac{1}{v}=kt+c[/tex]
'c' is the constant of integration whose value can be found out by putting value of 't' = 0 and noting V =4 m/s
Thus [tex]c=-\frac{1}{4}[/tex]
the value of 'k' can be found by using the fact that at t= 30 seconds velocity = 26 m/s
[tex]\frac{-1}{26}=k\times 30-\frac{1}{4}\\\\\therefore k=\frac{\frac{-1}{26}+\frac{1}{4}}{30}\\\\k=7.05\times 10^{-3}[/tex]
Hence the velocity as a function of time is given by
[tex]v(t)=\frac{-1}{7.05\times 10^{-3}t-\frac{1}{4}}[/tex]
By definition of velocity we have
[tex]v=\frac{dx}{dt}[/tex]
Making use of the obtained velocity function we get
[tex]\frac{dx}{dt}=\frac{-1}{kt-\frac{1}{4}}\\\\\int dx=\int \frac{-dt}{kt-\frac{1}{4}}\\\\x(t)=\frac{-1}{7.05\times 10^{-3}}\cdot ln(7.05\times 10^{-3}t-\frac{1}{4})+x_o[/tex]
here [tex]x_o[/tex] is the constant of integration
A heat engine is coupled with a dynamometer. The length of the load arm is 900 mm. The spring balance reading is 16. Applied weight is 500 N. Rotational speed is 1774. How many kW of power will be developed?
Answer:
P = 80.922 KW
Explanation:
Given data;
Length of load arm is 900 mm = 0.9 m
Spring balanced read 16 N
Applied weight is 500 N
Rotational speed is 1774 rpm
we know that power is given as
[tex] P = T\times \omega[/tex]
T Torque = (w -s) L = (500 - 16)0.9 = 435.6 Nm
[tex]\omega[/tex] angular speed [tex]=\frac{2 \pi N}{60} [/tex]
Therefore Power is
[tex]P =\frac{435.6 \time 2 \pi \times 1774}{60} = 80922.65 watt[/tex]
P = 80.922 KW
Steam at 1400 kPa and 350°C [state 1] enters a turbine through a pipe that is 8 cm in diameter, at a mass flow rate of 0.1 kg⋅s−1. The exhaust from the turbine is carried through a 15-cm-diameter pipe and is at 50 kPa and 100°C [state 2]. What is the power output of the turbine?
H1 = 3150.7 kJ/kg V1 = 0.2004 m3/kg
H2 = 2682.6 kJ/kg V2 = 3.4181 m3/kg
Answer:
Power output, [tex]P_{out} = 178.56 kW[/tex]
Given:
Pressure of steam, P = 1400 kPa
Temperature of steam, [tex]T = 350^{\circ}C[/tex]
Diameter of pipe, d = 8 cm = 0.08 m
Mass flow rate, [tex]\dot{m} = 0.1 kg.s^{- 1}[/tex]
Diameter of exhaust pipe, [tex]d_{h} = 15 cm = 0.15 m[/tex]
Pressure at exhaust, P' = 50 kPa
temperature, T' = [tex]100^{\circ}C[/tex]
Solution:
Now, calculation of the velocity of fluid at state 1 inlet:
[tex]\dot{m} = \frac{Av_{i}}{V_{1}}[/tex]
[tex]0.1 = \frac{\frac{\pi d^{2}}{4}v_{i}}{0.2004}[/tex]
[tex]0.1 = \frac{\frac{\pi 0.08^{2}}{4}v_{i}}{0.2004}[/tex]
[tex]v_{i} = 3.986 m/s[/tex]
Now, eqn for compressible fluid:
[tex]\rho_{1}v_{i}A_{1} = \rho_{2}v_{e}A_{2}[/tex]
Now,
[tex]\frac{A_{1}v_{i}}{V_{1}} = \frac{A_{2}v_{e}}{V_{2}}[/tex]
[tex]\frac{\frac{\pi d_{i}^{2}}{4}v_{i}}{V_{1}} = \frac{\frac{\pi d_{e}^{2}}{4}v_{e}}{V_{2}}[/tex]
[tex]\frac{\frac{\pi \times 0.08^{2}}{4}\times 3.986}{0.2004} = \frac{\frac{\pi 0.15^{2}}{4}v_{e}}{3.418}[/tex]
[tex]v_{e} = 19.33 m/s[/tex]
Now, the power output can be calculated from the energy balance eqn:
[tex]P_{out} = -\dot{m}W_{s}[/tex]
[tex]P_{out} = -\dot{m}(H_{2} - H_{1}) + \frac{v_{e}^{2} - v_{i}^{2}}{2}[/tex]
[tex]P_{out} = - 0.1(3.4181 - 0.2004) + \frac{19.33^{2} - 3.986^{2}}{2} = 178.56 kW[/tex]
The power output of the Turbine is; 225.69 kW
What is the Power Output?We are given
Pressure of steam; P = 1400 kPa
Temperature of steam at state 1; T = 350°C
Diameter of pipe; d₁ = 8 cm = 0.08 m
Mass flow rate; m' = 0.1 kg/s
Diameter of exhaust pipe; d₂ = 15 cm = 0.15 m
Pressure at exhaust; P' = 50 kPa
Temperature at state 2; T' = 100°C
Area; A = πd²/4
A = π * 0.08²/4
A = 0.0016π m²
We can find the find initial velocity from the formula;
v₁ = m' * V₁/A
v₁ = (0.1 * 0.2004/(0.0016π))
v₁ = 3.986 m/s
From equation of compressible fluid, we know that;
(A₁ * v₁)/V₁ = (A₂ * v₂)/V₂
A₂ = πd₂²/4
A₂ = π * 0.15²/4
A₂ = 0.005625π m²
(0.0016π * 3.986)/0.2004 = (0.005625π * v₂)/3.4181
Solving for v₂ gives;
v₂ = 19.33 m/s
Finally power output is gotten from the expression;
P_out = -m'(H₂ - H₁) + (v₂² - v₁²)/2
P_out = -0.1(2682.6 - 3150.7) + (19.33² - 3.986²)/2
P_out = 225.69 kW
Read more about Power Output at; https://brainly.com/question/25573309
Write a matrix, that is a lower triangular matrix.
Answer:
[tex]\left[\begin{array}{ccc}10&0&0\\14&25&0\\57&18&39\end{array}\right][/tex]
Explanation:
A lower triangular matrix is one whose elements above the main diagonal are zero meanwhile all the main diagonals elements and below are nonzero elements. This is one of the two existing types of triangular matrixes. Attached you will find a image referring more about triangular matrixes.
If there is any question, just let me know.
What is the range of a 32-bit signed integer?
Answer:
From -2147483647 to 2147483648.
Explanation:
A 32 bit integer has 2^32 = 4294967296 possible values. A signed integer has positive and negative values as well as the zero.
Of these values (2^32)/2 will be positive, (2^32)/2 - 1 will be negative and one will be the zero.
Therefore the range is from -(2^32)/2 + 1 to (2^32)/2.
This can also be expressed as from -2147483647 to 2147483648.
The Energy Losses Associated with Valves and Fittings: a)- are generally associated with a K factor b)- are generally associated with an external surface finish. c)- both answers 1 and 2 d)- all of the above.
Answer:
a)Are generally associated with factor.
Explanation:
We know that losses are two types
1.Major loss :Due to friction of pipe surface
2.Minor loss :Due to change in the direction of flow
As we know that when any hindrance is produced during the flow of fluid then it leads to generate the energy losses.If flow is along uniform diameter pipe then there will not be any loss but if any valve and fitting placed is the path of fluid flow due to this direction of fluid flow changes and it produce losses in the energy.
Lot' of experimental data tell us that loss in the energy due to valve and fitting are generally associated with K factor.These losses are given as
[tex]Losses=K\dfrac{V^2}{2g}[/tex]
A person is attempting to start a 20hp diesel engine with a hand crank. The distance from the handle to the center of rotation is 12 inches. The person is able to apply 25 lbf tangent to the circular path of the handle. The crank rotates at 2 rounds per second. How much power (Btu/min and hp) is the person providing?
Answer: 0.57 hp, 24.2 Btu/min
Explanation:
Hi!
The power P delivered when rotating a crank at angular speed ω, applying a torque τ is given by:
P = τ*ω
In this case torque is τ = 12 in * 25 lbf = 300 lbf*in
Angular speed is 2 round per seconds, which is 120 RPM. Then power is:
P = 300*120 lbf*in*RPM
1 hp = (lbf*in*RPM) / 63,025
P = 0.57 hp
1 hp = 42,4 Btu/min
Then P = 24.2 Btu/min
A(n)____ topology is the most reliable.
Answer:
Star topology
Explanation:
Topology:
Topology is the connection of networks .These network connect by nodes.
Type of topology:
1.Bus topology
2.Star topology
3.Ring topology
4.Mesh topology
Star topology is the most reliable topology .Because failure of node node does not affect the other nodes.In star topology network are connect in star form.
Ring topology is the most undesirable topology.In ring topology network connects in the ring form.In ring topology failure of one node affect the whole network.
Vernier calipers are capable of taking readings to the nearest 0.001 in. a)- True b)- false
Answer:
False
Explanation:
Vernier caliper is used for measuring very small distances. It is very precise instrument for measuring very small distances.
With the help of vernier caliper we can measure distances from 6 inch to about 12 inch
But in question we have given 0.001 in so it is impossible to measure 0.001 inch from vernier caliper so it is a false statement
A slight breeze is blowing over the hot tub above and yields a heat transfer coefficient h of 20 W/m2 -K. The air temperature is 75 F. If the surface area of the hot tub is 7.5 m2 , what is the heat loss (heat rate) due to convection? The temp of Hot Tube is 102F.
Answer:4050 W
Explanation:
Given
Heat transfer Coefficient(h)=[tex]20 W/m^2-K[/tex]
Air temperature =75 F
surface area(A)=[tex]7.5 m^2[/tex]
Temperature of hot tube is 102 F
We know heat transfer due to convection is given by
[tex]Q=hA\left ( \Delta T\right )[/tex]
[tex]Q=20\times 7.5\left ( 102-75\right )=4050 W[/tex]
Air at 20' C in the cylinder of a diesel engine is compressed from an initial pressure of 1 atm and volume of 800 cm3 to 60 cm3. Assume that air behaves as an ideal gas with γ-1.40 and that the compression is adiabatic. Find the final pressure and temperature of the air.
Answer:
The pressure is 37.56 atm.
Temperature at the end of adiabatic compression is 825.73 K.
Explanation:
Given that
[tex]T_1=20C[/tex]
[tex]P_1=1\ atm[/tex]
[tex]V_1=800\ cm^3[/tex]
[tex]V_2=60\ cm^3[/tex]
So r=800/60=13.33
γ=1.4
For process 1-2
[tex]\dfrac{T_2}{T_1}=r^{\gamma -1}[/tex]
[tex]\dfrac{T_2}{273+20}=13.33^{1.4-1}[/tex]
[tex]T_2=825.73\ K[/tex]
[tex]\dfrac{P_2}{P_1}=r^\gamma[/tex]
[tex]\dfrac{P_2}{1}=13.33^{1.4}[/tex]
[tex]P_2=37.56\ atm[/tex]
So
The pressure is 37.56 atm.
Temperature at the end of adiabatic compression is 825.73 K.
Relation between Poisson's ration, young's modulus, shear modulus for an isotropic material
Answer:
E=2 G(1+2μ)
Explanation:
Isotropic material :
Those material have same property in all direction is known as isotropic material.
Homogeneous material :
Those material have same property through out the volume is known as homogeneous material.
Relationship between Poisson ratio ,young modulus and shear modulus:
E=2 G(1+2μ)
Relationship between Poisson ratio ,bulk modulus and shear modulus:
E=2 K(1-μ)
Where
E is young modulus.
G is shear modulus.
μ is Poisson ratio.
Compute the fundamental natural frequency of the transverse vibration of a uniform beam of rectanqular cross section, with one end of the beam is free and one end is fixed. The cross section has a base of 100 mm and height of 300 mm, length of the beam is 5.9 m, E=20.5x10^10 N/m2 and density of 7830 kg/m3. Write your answer in rad/sec with 2 decimal points.
Answer:
The natural angular frequency of the rod is 53.56 rad/sec
Explanation:
Since the beam is free at one end and fixed at the other hence the beam is a cantilevered beam as shown in the attached figure
We know that when a unit force is placed at the end of a cantilever the displacement of the free end is given by
[tex]\Delta x=\frac{PL^3}{3EI}[/tex]
Hence we can write
[tex]P=\frac{3EI\cdot \Delta x}{L^3}[/tex]
Comparing with the standard spring equation [tex]F=kx[/tex] we find the cantilever analogous to spring with [tex]k=\frac{3EI}{L^3}[/tex]
Now the angular frequency of a spring is given by
[tex]\omega =\sqrt{\frac{k}{m}}[/tex]
where
'm' is the mass of the load
Thus applying values we get
[tex]\omega _{beam}=\sqrt{\frac{\frac{3EI}{L^{3}}}{Area\times density}}[/tex]
[tex]\omega _{beam}=\sqrt{\frac{\frac{3\times 20.5\times 10^{10}\times \frac{0.1\times 0.3^3}{12}}{5.9^{3}}}{0.3\times 0.1 \times 7830}}=53.56rad/sec[/tex]
Answer:
its a lil confusing
Explanation:
Consider a single pane window. The dimensions of the ¼-inch-thick glass window pane are about 0.9 m by 1.65 m. The surface temperatures of the glass will not be equal to the air temperature on the respective sides, as will be seen later in the course. For these conditions, the glass surface temperatures are approximately 1°F and -7°F. (At this time, we do not have the HT skills to calculate the surface temperatures.) Determine the heat transfer rate vector through the glass for these surface temperatures. Express your answer in vector notation. Your sketch should identify your coordinate system and your vector answer should agree with your sketch. For consistency, set your coordinate system such that the inside glass surface is at the origin and the outside surface is in the positive x direction (typically to the right!).
Answer:
q = (709*K*i + 0*j + 0*k)
Explanation:
1/4 inch is 6.35 mm = 0.00635 m
A = 0.9 * 1.65 = 1.48 m^2
t1 = 1 F = -17.2 C
t2 = -7 F = -21.7 C
The heat will be conducted through the glass. We use a frame of reference with the origin on the warmer side of the glass (t1) and the positive X axis pointing perpendicular to the glass towards the colder side.
The Fourier equation for plates (one dimensional form) is:
q = -K * dT / dx
We can simplify dT/dx to ΔT/Δx if we assume the temperature changes linearly through the glass.
q = -K * ΔT/Δx
K is the thermal conductivity of the glass
ΔT = t2 - t1
ΔT = -21.7 + 17.2 = -4.5 C
Δx is the thickness of the glass
q = -K * -4.5 / 0.00635
q = 709 * k
The vector is: q = (709*K*i + 0*j + 0*k)
It has no components in Y or Z because there if no variation of temperature in those directions (the temperature of the glass is given as each face having a constant temperature throughout its area).
Which of carbon will have higher strength but less ductility, 0.49% or 0.19%
Answer:
0.49%
Explanation:
Assuming this is about steel. Higher carbon steel tend to be harder and stronger, but that hardness makes them more brittle and less ductile. This is because with higher carbon concentrations there is more formation of pearlite, which has higher hardness than ferrite. Pearlite contains layers of cementite, which is a fragile material, so the presence of these microstructures will make the whole thing more brittle.
A flat plate that is 0.3m wide and 1m long is pulled over a film of water that is 0.2mm thick. The water is at 20 C. If the pulling force is 20N, what is the velocity of the plate?
Answer:
The velocity of the pulling plate is 14.98 m/s.
Explanation:
The shear stress caused by the 20 Newton force on the plate is given by
[tex]\tau =\frac{20}{Area}=\frac{20}{0.3\times 1.0}=66.66N/m^2[/tex]
Now by newton's law of viscosity we have
[tex]\tau =\mu\cdot \frac{\Delta u}{\Delta y}[/tex]
where
[tex]\mu [/tex] is the dynamic viscosity of the water at 20 degree
[tex]\frac{\Delta u}{\Delta y}[/tex] is the velocity gradient
Applying values we get
[tex]66.66=8.90\times 10^{-4}\times \frac{U}{0.2\times 10^-3}\\\\\therefore u=14.98m/s[/tex]
Determine the maximum weight of the flowerpot that can besupported without exceeding a cable tension of 50 lb in eithercable AB or AC.
Answer:
Maximum weight = 76.64 lb
Explanation:
In the second figure attached it can be seen the free body diagram of the problem.
The equation of equilibrium respect x-axis is
[tex] \sum F_x = 0 [/tex]
[tex] F_{AC} \times sin 30 - F_{AB} \times \frac{3}{5} = 0 [/tex]
[tex] F_{AC} = 1.2 \times F_{AB} [/tex]
So, cable segmet AC supports bigger tension than segment AB. If [tex] F_{AC} = 50 lb [/tex] then
[tex] F_{AB} = \frac{F_{AC}}{1.2} [/tex]
[tex] F_{AB} = 41.67 lb [/tex]
The equation of equilibrium respect y-axis is
[tex] \sum F_y = 0 [/tex]
[tex] F_{AB} \times \frac{4}{5} + F_{AC} \times cos 30 - W = 0 [/tex]
[tex] 41.67 lb \times \frac{4}{5} + 50 lb \times cos 30 - W = 0 [/tex]
[tex] W = 76.64 lb [/tex]
Write the chemical equation of the polymerization reaction to synthesize PS
Explanation:
Styrene is a vinyl monomer in which there is a carbon carbon double bond.
The polymerization of the styrene, which is initiated by using a free radical which reacts with the styrene and the compound thus forms react again and again to form polystyrene (PS).
The equation is shown below as:
[tex]\begin{matrix}& C_6H_5 \\&|\\n H_2C & =CH\end{matrix}[/tex] ⇒ [tex]\begin{matrix}&C_6H_5 \\&|\\ -[-H_2C & -CH-]-_n\end{matrix}[/tex]
A thin film of oil (v=0.001 m^2/s) 2mmthick flows down to
a surface inclined at 30 degrees to thehorizontal. What is the
maximum and mean velocity offlow?
Answer:
Maximum and mean velocity will be equal i.e 0.5 m/s
Explanation:
given data:
viscosity = 0.001 m^2/s
Thickness of thin film = 2 mm = 0.002 m
Neglecting the body weight hence no shear stress
Mean velocity is given V
[tex]V = \frac{\nu}{D}[/tex]
[tex]V = \frac{0.001}{2*10^{-3}}[/tex]
V = 0.5 m/s
Maximum and mean velocity will be equal i.e 0.5 m/s
The three major network category are_____,_____ and_____
Answer:
The three major network categories are LAN (Local Area Network), MAN (Metropolitan Area Network) and WAN (Wide Area Network)
Explanation:
A Local Area Network (LAN) is the simplest form of a network. It is usually limited to a geographical area and consists of a group of computers in the same organisation linked together. In most cases, the same technology is used for all computers in this network (eg. ethernet).
A Metropolitan Area Network (MAN) can connect multiple LANs as long as they are close to each other (geographically). MANs allow high speed remote connection as if the devices were on the same LAN.
A Wide Area Network (WAN) can connect multiple LANs across large geographical distances. Unlike MANs, the speed might differ based on factors such as distance. The internet is the most popular example of a WAN.
By increasing the cross-sectional area of the restriction, one can significantly increase the flow velocity. a) True b) False
Answer:
b)false
Explanation:
As we know that
Volume flow rate Q
Q = A x V
For constant volume flow rate,if velocity will increase then automatically area will decrease and vice versa.
Generally nozzle are used to increase the velocity and diffuser are used to decrease the exit velocity of flow.
So by increasing the cross sectional area of the restriction ,the velocity of the flow will decrease.
20 gallons of an incompressible liquid exert a force of 50 lbf at the earth’s surface. What force in lbf would 3 gallons of this liquid exert on the surface of the moon? The gravitational acceleration on the surface of the moon is 5.51 ft/s^2.
Answer:
1.29 lbf
Explanation:
Weight is a force, it is the product of a mass by the acceleration of gravity.
f = m * a
Gallons are a unit of volume. The relationship of volume with mass is:
m = V * δ
δ is the density (mass per unit of volume)
Then the weight of a liquid is:
w = V * δ * g
Rearranging:
δ = w / (V * g)
The acceleration of gravity on Earth is 32.2 ft/s^2
δ = 50 / (20 * 32.2) = 0.078 lbm/gallon
Knowing this and the gravity on the Moon we can calculate how much would 3 gallons of this liquid weight on the Moon.
w = V * δ * g
w = 3 * 0.078 * 5.51 = 1.29 lbf
Determine the activation energy for diffusing copper into gold if you know that the diffusion coefficient is 3.98 x 10-13 m2/s at 980 degreeC and the diffusion coefficient is 3.55 x 10-16 m2/s at 650degreeC.
Answer:
[tex]Q_d = 0.0166 J/mol[/tex]
Explanation:
given data:
diffusion coefficient [tex]= 3.98 \times 10^{-13} m^2/s[/tex]
[tex]T_1 = 980 Degree\ celcius = 1253 K[/tex]
[tex]T_2 = 650 Degree\ celcius = 923 K[/tex]
[tex]D_2 = 3.55\times 10^{-16} m^2/s[/tex]
Activation energy is given as[tex] = -2.3R \frac{ \Delta log D}{\Delta\frac{1}{T}}[/tex]
[tex] Q_d = -2.3 R [\frac{logD_1 - logD_2}{ \frac{1}{T_1} - \frac{1}{T_2}}][/tex]
[tex]Q_d = -2.3 \times 8.31 \frac{log(3.98*10^{-13} - log(3.55*10^{-16}}{ \frac{1}{1253} - \frac{1}{923}}[/tex]
[tex]Q_d = 0.0166 J/mol[/tex]
It is said that Archimedes discovered the buoyancy laws when asked by King Hiero of Syracuse to determine whether his new crown was pure gold (SG = 19.3). Archimedes measured the weight of the crown in air to be 11.8 N and its weight in water to be 10.9 N. Was it pure gold?
Answer with Explanation:
The crown will be pure if it's specific gravity is 19.3
Now by definition of specific gravity it is the ratio between the weight of an object to the weight of water of equal volume
Since it is given that the weight of the crown is 11.8 N we need to find it's volume
Now According to Archimedes principle when the crown is immersed into water the water shall exert a force in upwards direction on the crown with a magnitude equaling to weight of the water displaced by the crown
Mathematically this is the difference between the weight of the crown in air and weight when immersed in water
Thus Buoyant force is [tex]F_{B}=11.8-10.9=0.9N[/tex]
Now by Archimedes principle This force equals in magnitude to the weight of water of same volume as of the crown
Thus the specific gravity of the crown equals
[tex]S.G=\frac{11.8}{0.9}=13.11[/tex]
As we see that the specific gravity of the crown material is less than that of pure gold hence we conclude that it is impure.
Given:
[tex]\to SG_{gold} = 19.3 \\\\[/tex]
weight of air [tex]W_{air} = 11.8\ N \\\\[/tex]
water weight [tex]W_{water} = 10.9 \ N \\\\[/tex]
To Find:
using the buoyancy B that calculates the difference of weight=?
Solution:
Using formula:
[tex]\to B = W_{air} - W_{water} \\\\[/tex]
[tex]= 11.8\ N - 10.9\ N\\\\ = 0.9 \ N\\\\[/tex]
Using a formula for calculating weight:
[tex]\to W_{air} = SG_{\gamma water}\times V_{crown}\\\\ \to W_{water} = B(SG - 1)[/tex]
calculating the [tex]\bold{SG_{crown}}[/tex]:
[tex]\to SG_{crown}=1+\frac{W_{water}}{B} \\\\[/tex]
[tex]= 1 + \frac{10.9\ N}{0.9\ N}\\\\= 1 + 12.11\\\\= 13.11[/tex]
Knowing that the [tex]SG_{gold}= 19.3[/tex] indicates that the crown is not made of pure gold.
[tex]\to \bold{SG_{crown}= 13.1}[/tex] The crown is not composed entirely of gold.
Find out more information about the gold here:
brainly.com/question/900003
The hoist of a crane consists of a 10 kW electric motor running at 1440 rpm drivine 300 mm diameter drunn through a 60:1 gear reduction unit. If the efficiency is 90% . calculate the load, in tonnes that can be lifted at the rated motor capacity, and the lifting speed.
Answer:
Load = 2.42 tons
Lifting speed = 24 RPM
Explanation:
Given that
Power=10 KW
Efficiency = 90%
So the actual power,P=0.9 x 10 =9 KW
Speed of motor = 1440 RPM
Diameter of drum = 300 mm
radius =150 mm
G=60:1
Lets take speed of drum =N
We know that
[tex]G=\dfrac{Speed\ of\ motor}{Speed\ of\ drum}[/tex]
[tex]60=\dfrac{1440}{N}[/tex]
N=24 RPM
We know that
[tex]P=\dfrac{2\pi NT}{60}[/tex]
Where T is the torque
[tex]9000=\dfrac{2\pi \times 24\times T}{60}[/tex]
T=3580.98 N.m
Lets take load =F
So T= F x r
3580.98 = F x 0.15
F=23.87 KN
We know that
1 KN=0.109 tons
So 23.87 KN= 2.42 tons
So the load = 2.42 tons
Lifting speed = 24 RPM
A rigid tank holds 10 lbm of 160 °F water. If the quality of the water is 0.5 then what is the pressure in the tank and volume of the tank?
Answer:
The pressure and volume of the tank are 4.74703 psi and 385.968 ft³ respectively.
Explanation:
Volume is constant as the tank is rigid. Take the saturation condition of water from the steam table for pressure at 160°F.
Given:
Mass of the water is 10 lb.
Dryness fraction is 0.5.
Temperature of water is 160°F.
From steam table at 160°F:
The pressure in the tank is 4.74703 psi.
Specific volume of saturated water is 0.0163918 ft³/lb.
Specific volume of saturated steam is 77.1773 ft³/lb.
Calculation:
Step1
From steam table at 160°F:
The pressure in the tank is 4.74703 psi.
Step2
Specific volume of tank is calculated as follows:
[tex]v=v_{f}+x(v_{g}-v_{f})[/tex]
[tex]v=0.0163918 +0.5(77.1773 -0.0163918)[/tex]
[tex]v=0.0163918 +38.58045[/tex]
v=38.5968 ft³/lb.
Step4
Volume is calculated as follows:
[tex]V=v\times m_{t}[/tex]
[tex]V=38.5968\times10[/tex]
V=385.968 ft³.
Thus, the pressure and volume of the tank are 4.74703 psi and 385.968 ft³ respectively.
Air flows at 45m/s through a right angle pipe bend with a constant diameter of 2cm. What is the overall force required to keep the pipe bend in place? Is it: a) 0.76 N b) 1.08 N c) 1.52 N d) 0.25 N e) 2.56 N
Answer:
b)1.08 N
Explanation:
Given that
velocity of air V= 45 m/s
Diameter of pipe = 2 cm
Force exerted by fluid F
[tex]F=\rho AV^2[/tex]
So force exerted in x-direction
[tex]F_x=\rho AV^2[/tex]
[tex]F_x=1.2\times \dfrac{\pi}{4}\times 0.02^2\times 45^2[/tex]
F=0.763 N
So force exerted in y-direction
[tex]F_y=\rho AV^2[/tex]
[tex]F_y=1.2\times \dfrac{\pi}{4}\times 0.02^2\times 45^2[/tex]
F=0.763 N
So the resultant force R
[tex]R=\sqrt{F_x^2+F_y^2}[/tex]
[tex]R=\sqrt{0.763^2+0.763^2}[/tex]
R=1.079
So the force required to hold the pipe is 1.08 N.
How much calcium chloride will react with100mg of soda ash?
Answer:
105mg of calcium chloride [tex]CaCl_{2}[/tex]
Explanation:
The molecular formula of calcium chloride is [tex]CaCl_{2}[/tex] and the molecular formula of soda ash is [tex]Na_{2}CO_{3}[/tex]
First of all you should write the balanced reaction between both compounds, so:
[tex]CaCl_{2}+Na_{2}CO_{3}=2NaCl+CaCO_{3}[/tex]
Then you should have the molar mass of the two compounds:
Molar mass of [tex]CaCl_{2}=110.98\frac{g}{mol}[/tex]
Molar mass of [tex]Na_{2}CO_{3}=105.98\frac{g}{mol}[/tex]
Now with stoichiometry you can find the mass of calcium chloride that reacts with 100mg of soda ash, so:
[tex]100mgNa_{2}CO_{3}*\frac{1molNa_{2}CO_{3}}{105.98gNa_{2}CO_{3}}*\frac{1molCaCl_{2}}{1molNa_{2}CO_{3}}*\frac{110.98gCaCl_{2}}{1molCaCl_{2}}=105mgCaCl_{2}[/tex]
For an orthogonal cutting operation, tool material is HSS, rake angle is 15° , chip thickness is 0.5 mm, speed is 55 m/min and feed is 0.3 mm/rev. The shear plane angle (in degrees) is
Answer:
The shear plane angle is 34.45°.
Explanation:
Orthogonal cutting is the cutting process in which cutting direction or cutting velocity is perpendicular to the edge of the surface. For orthogonal cutting operation feed is the chip thickness.
Given:
Rake angle is 15°.
Uncut chip thickness is 0.5 mm.
Speed is 55 m/min.
Feed or the chip thickness is 0.3 mm.
Calculation:
Step1
Chip reduction ratio is calculated as follows:
[tex]r=\frac{t_{c}}{t}[/tex]
[tex]r=\frac{0.3}{0.5}[/tex]
r = 0.6
Step2
Shear angle is calculated as follows:
[tex]tan\phi=\frac{rcos\alpha}{1-rsin\alpha}[/tex]
Here, [tex]\phi[/tex] is shear plane angle, r is chip reduction ratio and [tex]\alpha[/tex] is rake angle.
Substitute all the values in the above equation as follows:
[tex]tan\phi=\frac{rcos\alpha}{1-rsin\alpha}[/tex]
[tex]tan\phi=\frac{0.6cos15^{\circ}}{1-0.6sin15^{\circ}}[/tex]
[tex]tan\phi=\frac{0.57955}{0.8447}[/tex]
[tex]\phi=34.45^{\circ}[/tex]
Thus, the shear plane angle is 34.45°.
Under a construction management (CM) contract, should the CM firm's responsibilities normally begin at the construction phase, the design phase, the planning phase, or the conceptual phase?
The CM firm's responsibilities under a construction management contract should begin at the planning phase. This early engagement allows for a cohesive approach to project management, involving definition of scope, budgeting, and risk assessment. Construction managers work closely with designers and contractors throughout the project, ensuring it meets design specifications and safety standards.
Explanation:Under a construction management (CM) contract, the CM firm's responsibilities should begin at the planning phase, which precedes the design phase, construction phase, and conceptual phase. During the planning phase, the CM firm is involved in defining project objectives, scope, and feasibility, providing valuable input that shapes the overall project. The expertise of construction managers is utilized to help with site selection, project scheduling, budgeting, and risk management. Their early involvement ensures that the construction phase flows more smoothly, as potential issues may have been identified and addressed beforehand. Construction managers play a crucial role in maintaining the integrity of the design and adherence to specifications throughout the construction process.
Designers, on the other hand, continue their involvement even after generating detailed technical drawings and digital models by acting as on-site supervisors during construction. Their responsibility remains to ensure that contractors follow the design's specifications, indicating direct involvement in the contract construction phase. The construction site can present various risks, including the exposure of workers to dangerous materials which designers need to consider while specifying project materials. The collaborative effort between the CM firm, designers, and contractors is fundamental to achieving a successful and safe project completion, fulfilling the client's expectations, and managing any equity issues related to contract allocations.
Momentum is a conserved quantity for any general control volume. a)- True b)- False
Answer:
The given statement is false.
Explanation:
The basic equation of motion for a control volume is as follows
[tex]\frac{d\overrightarrow{p}}{dt}=\int_{c.v}\frac{\partial }{\partial t}(\rho v)dV+\int_{cs}(\rho \overrightarrow{v})\cdot \overrightarrow{v_{r}}.\widehat{n}dS[/tex]
the symbols have the usual meaning as
[tex]\rho [/tex] is density of the fluid
[tex]v [/tex] is the velocity of the fluid
[tex]\widehat{n}[/tex] is the direction vector of area over which the integration is carried out
As we see that the terms in the right hand side of the equation is not zero if the flow is unsteady or the velocity is changing in the control volume the term in the left is non zero hence the momentum is not conserved.