A wastewater treatment plant has two primary clarifiers, each 20m in diameter with a 2-m side-water depth. the effluent weirs are inboard channels set on a diameter of 18m. for a flow of 12900m^3/d, calculate the overflow rate, detention time,and weir loading.

Answer: 139 Km.

Explanation:

The question tells us that a planet A has an orbit period of 10 years and its circular orbit has a radius of 106 Km, whilst a planet B has an orbit period of 15 years (also assuming a circular orbit), both orbiting a nearby star.

This information allow us to use the Kepler's 3rd law, for the special case in which the orbit is circular.

Kepler's 3rd law, tells that there exist a direct proportionality between the square of the orbit period, and the cube of the orbit radius (in the more general case, with the cube of the semi-major axis of the elipse), for celestial bodies orbiting a same star.

(like Earth and Mars orbiting Sun).

So, for planet A and planet B (orbiting a same star), we can write the following:

(TA)²/ (TB)² = (rA)³ / (rB)³

Replacing by TA= 10 years, TB= 15 years, rA= 106 Km, and solving for Rb, we get  RB= 139 Km.

Answer:

Explanation:

A renewable energy source is one that can not depelted in a reasonable timeframe.

Sun energy will last until the Sun dies, which is expected to haen in about 5 billion years. Because it will last so long it is considered practiacally eternal and undepleteable.

Fossil fuels on the other hand are material deposits in the crust of Earth that might be depleted within centuries.

A renewable energy source can be replenished rapidly and is not permanently consumed by human use, examples include solar and wind energy. Fossil fuels like coal, oil, and natural gas are non-renewable because they take millions of years to form and are finite. Sustainable energy use does not exhaust resources and can continue over time.

A renewable energy source is defined as one that can be replenished in a short amount of time and is not permanently depleted by human usage. Renewable resources include things like solar and wind energy, which are continually available through natural processes such as sunlight and wind currents.

Coal, oil, and natural gas are not considered renewable energy sources because they are formed over millions of years from the buried remains of plants and animals. These fossil fuels are finite and once consumed, they do not replenish in a timeframe that is practical for human use, thereby classifying them as non-renewable.

When we use renewable resources, they offer a sustainable way to generate energy. Sustainable means using methods that do not completely use up or destroy natural resources, therefore capable of continuing for a long time. Examples of methods to harness renewable resources include solar panels for sunlight, wind turbines for wind, and hydroelectric power stations for flowing water.

Answer:

Diameter of the piston will be [tex]3.1847\times 10^{-3}m[/tex]

Explanation:

We have given force F = 0.2 kN = 200 N

Pressure P = 80 kPa = 80000 pa

We have to find the diameter of the piston

We know that [tex]pressure = \frac{force}{area }=\frac{200}{80000}=2.5\times 10^{-3}m^2[/tex]

We know that area of circular piston is given by [tex]A=\pi r^2[/tex]

So [tex]2.5\times 10^{-3}=3.14\times r^2[/tex]

[tex]r=1.5923\times 10^{-3}m[/tex]

We know that diameter d = 2×radius =[tex]d=1.5923\times 10^{-3}\times 2=3.1847\times 10^{-3}m[/tex]

Answer:

[tex]\phi =\dfrac{\Delta L}{h}[/tex]

Explanation:

Normal strain :

 It is the ratio of deformation to the original dimension.Normal strain occurs due to longitudinal force.

 Normal strain = ΔL/L

Shear strain:

It is the ratio of deformation to perpendicular dimension.Shear strain occurs due to tangential force.

From the second diagram:

[tex]tan\phi =\dfrac{\Delta L}{h}[/tex]

if angle Φ is small then we can write

[tex]tan\phi =\phi[/tex]

So

[tex]\phi =\dfrac{\Delta L}{h}[/tex]

This is the shear strain equation.

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

Explains how to calculate power output and cold reservoir temperature for a heat engine.

Given:

(a) Calculation of Power Output:

The efficiency formula for a heat engine is Efficiency = (Useful work output / Heat input). Power output can be calculated as Power output = Efficiency * Power input.

(b) Calculation of Temperature of Cold Reservoir:

Using the Carnot efficiency formula, you can find the cold reservoir temperature when the efficiency of the real heat engine is known.

Answer:

133.276 Btu/lbm

Explanation:

1 kJ/kg = 0.429923 Btu/lbm

Therefore, 310 kJ/kg = 133.276 Btu/lbm

Specific internal energy can be defined as the internal energy (kJ or Btu) divided by a unit of mass (kg or lbm). Both sets of units (kJ/kg and Btu/lbm) are units for specific energy.

Energy is an object's ability to do work and is represented in this example in Joules (J) or British Thermal Units (Btu).

1 kJ = 1000 J

Mass tells us how much something weighs and is represented in this example in kg or lbm (pounds).

Answer:

(a)27.12 N-m (b) 69.96 [tex]KN/m^3[/tex] (c) 1.27 mm/sec

Explanation:

We have to convert

(a) 20 lb-ft to N-m

We know that 1 lb = 4.45 N

So 20 lb = 20×4.45 = 89 N

1 feet = 0.3048 m

So [tex]20lb-ft=20\times 4.45N\times 0.3048N=27.12N-m[/tex]

(b) 450 [tex]lb/ft^3[/tex] to KN/[tex]m^3[/tex]

We know that 1 lb = 4.45 N = 0.0044 KN

[tex]1ft^3=0.0283m^3[/tex]

So [tex]450lb/ft^3=\frac{450\times 0.0044KN}{0.0283m^3}=69.96KN/m^3[/tex]

(c) 15 ft/hr to mm/sec

We know that 1 feet = 0.3048 m = 304.8 mm

And 1 hour = 60×60=3600 sec

So [tex]15ft/h=\frac{15\times 304.8mm}{3600sec}=1.27 mm/sec[/tex]

Answer:

a)20 lb.ft=27.2 N.m

b)[tex]450\dfrac{lb}{ft^3}=70.65\dfrac{KN}{m^3}[/tex]

c)15 ft/h = 1.26 mm/s

Explanation:

a)

As we know that

1 ft.lb= 1.36 N.m

So 20 lb.ft = 1.36 x 20 N.m

20 lb.ft=27.2 N.m

b)

We know that

[tex]1\dfrac{lb}{ft^3}=0.157\dfrac{KN}{m^3}[/tex]

So

[tex]450\dfrac{lb}{ft^3}=450\times 0.157\dfrac{KN}{m^3}[/tex]

[tex]450\dfrac{lb}{ft^3}=70.65\dfrac{KN}{m^3}[/tex]

c)

As we know that

1 ft/h=0.084 mm/s

So

15 ft/h = 0.084 x 15 mm/s

15 ft/h = 1.26 mm/s

Answer:

Explanation:

Given

diameter(d)=1.1 m

mean velocity(u)=50 cm/s

mass flow rate(m)=110 kg/s

[tex] A=0.950 m^2[/tex]

[tex]m=\rho \cdot A\cdot u[/tex]

where [tex]\rho [/tex] =density of fluid

[tex]110=\rho \times 0.95\times 0.5[/tex]

[tex]\rho =231.46 kg/m^3[/tex]

Therefore specific gravity[tex]=\frac{\rho }{\rho _{water}}[/tex]

[tex]=\frac{231.46}{1000}=0.231[/tex]

Specific weight[tex]=\rho \cdot g=231.46\times 9.81=2270.70 kg/m^2-s^2[/tex]

specific volume[tex]=\frac{1}{density}[/tex]

[tex]=\frac{1}{231.46}=0.00432 m^3/kg[/tex]

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.

Explanation:

A ductile material can convert into brittle material due to following reasons

1.At very low temperature

2.Due to presence of notch

In titanic ,the base of ship strike to the large ice cube and lower part of titanic ship material was made of steel .We know that steel is ductile material and when steel came with very low temperature of ice due to this ductile material converted in to brittle material and titanic ship failed.Brittle material does not show any indication before failure.

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.

Answer:

Explanation:

Given

Force=9 kN

Diameter reduces from 7 mm to 5 mm

As volume remains constant therefore

[tex]A_0L_0=A_fL_f[/tex]

[tex]7^2\times L_0=5^2\times L_f[/tex]

[tex]\frac{L_0}{L_f}=\frac{25}{49}[/tex]

Thus Engineering Strain [tex]\epsilon _E=\frac{L_f-L_0}{L_0}[/tex]

[tex]=\frac{49}{25}-1=\frac{49-25}{25}=0.96[/tex]

Engineering stress[tex]=\frac{Load}{original\ Cross-section}[/tex]

[tex]\sigma _E=\frac{9\times 10^3}{\frac{\pi 7^2}{4}}=233.83 MPa[/tex]

(b)True stress

[tex]\sigma _T=\sigma _E\left ( 1+\epsilon _E\right )[/tex]

[tex]\sigma _T=233.83\times (1+0.96)=458.30 MPa[/tex]

True strain

[tex]\epsilon _T=ln\left ( 1+\epsilon _E\right )[/tex]

[tex]\epsilon _T=ln\left ( 1.96\right )=0.672[/tex]

Answer:

26 lbf

Explanation:

The mass of the satellite is the same regardless of where it is.

The weight however, depends on the acceleration of gravity.

The universal gravitation equation:

g = G * M / d^2

Where

G: universal gravitation constant (6.67*10^-11 m^3/(kg*s))

M: mass of the body causing the gravitational field (mass of Earth = 6*10^24 kg)

d: distance to that body

15000 miles = 24140 km

The distance is to the center of Earth.

Earth radius = 6371 km

Then:

d = 24140 + 6371 = 30511 km

g = 6.67*10^-11 * 6*10^24 / 30511000^2 = 0.43 m/s^2

Then we calculate the weight:

w = m * a

w = 270 * 0.43 = 116 N

116 N is 26 lbf

Answer:

Explanation:

Convection needs a fluid to transport the heat, while radiation doesn't.

Generally convection transports a lot more heat than radiation.

Since fluids tend to expand, when in a gravitational field such as that of Earth convection tends to move heat upwards while radiation is indifferent to gravity.

Answer:

Total elongation will be 0.012 m

Explanation:

We have given diameter of the cylinder = 2.1 mm

Length of wire [tex]L=3.2\times 10^4mm[/tex]

So radius [tex]r=\frac{d}{2}=\frac{2.1}{2}=1.05mm=1.05\times 10^{-3}m[/tex]

Load F = 280 N

Elastic modulus = 207 Gpa

Area of cross section [tex]A=\pi r^2=3.14\times (1.05\times 10^{-3})^2=3.461\times 10^{-6}m^2[/tex]

We know that elongation in wire is given by [tex]\delta =\frac{FL}{AE}[/tex], here F is load, L is length, A is area and E is elastic modulus

So [tex]\delta =\frac{FL}{AE}=\frac{280\times 32}{3.461\times 10^{-6}\times 207\times 10^9}=0.012m[/tex]

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]

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).

Answer:

The mass of car in slug =108.5 slug.

The mass of car in kilogram =1575 Kg.

Explanation:

Given that

Mass of car = 3500 lbs

We know that

1 lbs =0.031 slug

So

3500 lbs = 0.031 x 3500 slug

So the mass of car in slug =108.5 slug.

We know that

1 lbs =0.45 kilograms

so

3500 lbs = 3500 x 0.45 Kg

So the mass of car in kilogram =1575 Kg.

Answer:

[tex]S_{10}=133.3m\\a_{10}=4.589m/s^{2}[/tex]

Explanation:

In order to know the value of the speed at any time t, we need to integrate the acceleration. Once we get the speed vs time, we need to integrate again to get the distance traveled by the motorcycle vs time. So let's start with the speed first:

[tex]V(t) = \int {a(t)} \, dt =  \int {2+0.2*t} \, dt = 2*t + 0.2*\frac{t^{2}}{2}[/tex]

We will integrate once again to get distance:

[tex]S(t) = \int {V(t)} \, dt = \int {2*t+0.2*\frac{t^{2}}{2} } \, dt  = t^{2}+0.2*\frac{t^{3}}{6}[/tex]

Now we just need t evaluate S(10s):

S(10) = 133.3m

For the acceleration, we know that:

[tex]a = \sqrt{a_{t}^{2}+a_{N}^{2}}[/tex]

where [tex]a_{t}(10)=2+0.2*(10)=4m/s^{2}[/tex]

and [tex]a_{N}(10)=\frac{V(10)^{2}}{R}=2.25m/s^{2}[/tex]

So, finally:

[tex]a = \sqrt{a_{t}^{2}+a_{N}^{2}} = 4.589m/s^{2}[/tex]

Answer:

Part B will be 37.2 m to the east of the launch point at an altitude of 80.8 m

Explanation:

At t0 the rocket is at 60 m and has a speed of 28 m/s.

Then it explodes when it reaches max altitude.

Since the rocket will have its engine off after t0 it will be in free fall.

It will be affected only by the acceleration of gravity, so it moves with constant acceleration, we can use this equation.

Y(t) = Y0 + V0*t + 1/2*a*t^2

Y0 = 60 m

V0 - 28 m/s

a = g = -9.81

We also have the equation for speed:

V(t) = V0 + a*t

And we know that when it reaches its highest point it ill have a speed of zero.

0 = V0 + a * t

a * t = -V0

t = -V0 / a

t = -28 / -9.81 = 2.85 s

This is the time after t0 when the engine ran of of fuel.

Using this value on the position equation:

Y(2.85) = 60 + 28*2.85 + 1/2*(-9.81)*2.85^2 = 100 m

At an altitude of 100 m it explodes in two parts. An explosion is like a plastic collision in reverse, momentum is conserved.

Since the speed of the rocket is zero at that point, the total momentum will be zero too.

Part A, with a mass of 1 kg fell 74.4 m west of the launch point. It fell in a free fall with a certain initial speed given to it by the explosion. This initial speed had vertical and horizontal components.

First the horizontal. In the horizontal there is no acceleration (ignoring aerodynamic drag).

X(t) = X1 + Vx1 * (t - t1)

X1 = 0 because it was right aboce the launch point. t1 is the moment of the explosion.

t1 = 2.85 s

We know it fell to the ground at t = 5.85 s

Vx1 * (t2 - t1) = X(t2) - X1

Vx1 = (X(t2) - X1) / (t2 - t1)

Vx1 = (74.4 - 0) / (5.85 - 2.85) = 24.8 m/s

Now the vertical speed

Y(t2) = Y1 + Vy1*(t2 - t1) + 1/2*a*(t2 - t1)^2

Vy1*(t2 - t1) = Y(t2) - 1/2*a*(t2 - t1)^2 - Y1

Y(t2) = 0 because it is on the ground.

Vy1 = (-1/2*a*(t2 - t1)^2 - Y1) / (t2 - t1)

Vy1 = (-1/2*-9.81*(5.85 - 2.85)^2 - 100) / (5.85 - 2.85) = -18.6 m/s

If the part A had a speed of (24.8*i - 18.6*j) m/s, we calcultate the speed of part 2

Horizontal:

vxA * mA + vxB * mB = 0

-vxA * mA = vxB * mB

vxB = -vxA * mA / mB

vxB = -24.8 * 1 / 2 = -12.4 m/s

Vertical:

vyA * mA + vyB * mB = 0

-vyA * mA = vyB * mB

vyB = -vyA * mA / mB

vyB = -(-16.6) * 1 / 2 = 8.3 m/s

Now that we know its speed and position at t1 we can know ehre it will be at t2

X(t) = 0 - 12.4 * (t - t1)

X(5.85) = -12.4 * (5.85 - 2.85) = -37.2 m

Y(t) = 100 + 8.3 * (t - t1) + 1/2 * (-9.8) * (t - t1)^2

Y(t) = 100 + 8.3 * (5.85 - 2.85) + 4.9 * (5.85 - 2.85)^2 = 80.8 m

Part B will be 37.2 m to the east of the launch point at an altitude of 80.8 m

Answer:

The nail exerts a force of 573.88 Pounds on the Hammer in positive j direction.

Explanation:

Since we know that the force is the rate at which the momentum of an object changes.

Mathematically [tex]\overrightarrow{F}=\frac{\Delta \overrightarrow{p}}{\Delta t}[/tex]

The momentum of any body is defines as [tex]\overrightarrow{p}=mass\times \overrightarrow{v}[/tex]

In the above problem we see that the moumentum of the hammer is reduced to zero in 0.023 seconds thus the force on the hammer is calculated using the above relations as

[tex]\overrightarrow{F}=\frac{m(\overrightarrow{v_{f}}-\overrightarrow{v_{i}})}{\Delta t}[/tex]

[tex]\overrightarrow{F}=\frac{m(0-(-73.33)}{0.23}=\frac{1.8\times 73.33}{0.23}=573.88Pounds[/tex]

Answer:

[tex]F = \frac{m * v^2}{r}[/tex]

Explanation:

Once the centrifugal forces are equivalent as an object rotates, it is called "in equilibrium." If the point of impact of the moving object does not align with the center of the rotation, unequal centrifugal forces are produced and the rotating component is "out of equilibrium."  

Two conditions for balanced condition are: static and coupled. Static equilibrium relates to a one plane mass in which the unit is balanced by  weight inverse the unbalanced mass

formula used to calculate centrifugal mass is [tex]F = \frac{m * v^2}{r}[/tex]

where, m is mass, v is speed of body. r is radius

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

Answer and Explanation:

SPECIFIC HEAT :

Answer:

2.67 hours

Explanation:

If three quarters of the mass are in liquid phase, I have  a mass of water:

m1 = 3/4 * 5 = 3.75 kg

The latent heat of vaporization of water is of

ΔHvap = 2257 kJ/kg

The heat needed to vaporize it is:

Q = m * ΔHvap

Q = 3.75 * 2257 = 8464 kJ

If I have a resistor connected to 110 V, with a current of 8 A, the heat it dissipates through Joule effect will be:

P = I * V

P = 8 * 110 = 880 W = 0.88 kW

With that power it will take it

t = Q / P

t = 8464/0.88 = 9618 s = 160 minutes = 2.67 hours2.

Answer:

1000000 watts

Explanation:

1 kJ/sec= 1000 watts (or 1 watt= 0.001 kJ/sec)

Therefore,

1000 kJ/sec = 1000 x 1000 watts

                    = 1000000 watts

A kJ/sec (Kilojoule per second) is a unit used to measure power. It comes from the SI (Standard International) unit J/sec (Joule per second).

1 J/sec= 1 watt

Power is the energy transferred by a force per unit of time.

Energy is measured in Joules.

In this question, we are working out how much energy is transferred in watts.

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.

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.

Answer:

a)True

Explanation:

The temperature at which the polymer becomes viscous is called glass transition temperature.

When polymer is heated then it will become viscous and temperature is called glass transition temperature.

Glass temperature depends on the chemical structure of the polymer.

Polymer are made of long change structure and these change are connected together one by one and form a complex structure.

Example -Rubber or elastomer,Plastics.