15 - Question 11 by Kambiz Ehsani - Thermodynamics - Turbines - 4/27/2018 - Solved

Calculate the hp of a steam turbine with the known inlet exhaust and bleed mass flow rates in pounds per hour.

Solution:

In Turbines with the Bleed the Turbine work is :

Wt = (Hinlet - Hbleed) + (1 - y) Hbleed - (1 - y) Hexhaust

y = bleed ratio = m dot bleed / mdot inlet

Wt = (Hinlet - Hbleed) + (1 - y) (Hbleed - Hexhaust )

Wt will be in Btu/hr to hp multiply by 3.939 E-4  hp / (Btu/hr)

14 - Question 10 by Kambiz Ehsani - General physics - 4/27/2018 - Solved

At what degree Rankine the value for the degree C and F will be equal?

Solution:

C = (5/9) * ( F - 32)
F = (9/5) * C + 32

(5/9) * ( T - 32) = (9/5) * T + 32

T = - 40 deg C or F  = 420 R

13 - Question 9 by Kambiz Ehsani - First Lat of the Thermodynamics - Pressure washer problem - 4/27/2018 - Solved

What is the increase of water temperature in the water being pumped by a pressure washer pump at a car wash? The inlet water temperature at the inlet of the pump is 70 degree F. We know that the pressure of the pump is 3000 psig. Please elaborate on your assumptions.

Solution:
In the absence of other information, it is common sense that the pump is adiabatic and isentropic. For isentropic compression and no change in Kinetic and Potential, the steady flow energy equation (SFEE) gives:

Wpump = m * (h2 -h1) = m * v * (v2 - v1)

Where :
v = specific volume of inlet water
v = 0.01672 ft^3 / lbm  (Sat. H20 at 1 atm)

and :
 p2 = 3000 lbf/ft^2
p1 = 14.7 lbf/inch^2

Then:
from the definition of c_p Delta _T
Delta _T = (9.2 Btu/lbm) / (1 Btu/lbm) = 9.2 Degree

Tout = 70 F + 9.2 F = 79.2 Degree F

12- Question 8 by Kambiz Ehsani - Second Law of the Thermodynamics - 4/27/2018 - Solved

The question was adopted from the Van Wylen Textbook 3rd edition:

A cyclic machine is used to transfer heat from a higher to a lower temperature reservoir, as show in the picture below.Determine if this machine with the energy transfer,values as shown , is reversible or irreversible or impossible.

Solution;

You have to examine the cycle for the Carnot cycle. For the given TH  , TL

Then the Carnot cycle efficiency will be = ( TH  - TL ) / TH = 1000 - 400 / 1000 = 0.60

Efficiency of the given system = Wnet / Qh = 0.615  > Carnot Efficiency or 0.6

Impossible

11- Question 7 by Kambiz Ehsani - Machine Design - 4/26/2018 - Solved

Design the K factor of the old revolver so that the initial speed of the bullet before it exit the gun become Vb2.
The known values are as following:

1. The length of the spring at the normal situation is L1
2. The length of the spring at the normal situation is L2
3. The Weight of the hammer piece is Mh
4.  Bullet initial speed is zero or Vb1 = 0
5. Vb2 is the velocity of the bullet after the impact is known
6. At the time of impact the velocity of the hammer will be Vh1
7. Bullet mass is know and that is Mb

Solution: (Parametric)

Start from the conservation of energy for the spring and hammer system:

Potential Energy absorbed in the Spring before pulling the trigger = 0.5 * K* L1^2

Potential Energy absorbed in the Spring after the impact = 0.5 * K * L2^2

Kinetic Energy at the time of the impact = 0.5 * Mh * Vh1^2 

Energy Conservation => Total energy before pulling the trigger  = Total energy at the time of impact

0.5 * K* L1^2 = 0.5 * K * L2^2 + 0.5 * Mh * Vh1^2         Eq (1)

K = (Mh * Vh1 ^2) / (L2 ^2 - L1^2)                                    Eq (2)

Conservation of the momentum => 

1. Vb1 is the velocity of the bullet before the impact was zero 
2. Vb2 is the velocity of the bullet after the impact is known
3. Vh1 is unknown
4. Vh2 is assumed to be zero after the impact

Mh * Vh1 = Mb2 * Vb2                                                    Eq (3)

Rearranging :

Vh1 = Mb2 * Vb2 / Mh1                                                     Eq (4)

Substituting Vh1 from Eq (4) in Eq (2)

K = Mh * (Mb2 * Vb2 / Mh) ^ 2 / (L2^2 - L1^2)

10- Question 6 by Kambiz Ehsani - Gravity between two bodies - 4/26/2018 - Solved

Which one of the following statements are true for the a ship passing by another one with little space between them?

A) There is a force pushing them away from each other
B) There is a force pulling them toward eachother
C) Due to the boundary layer the speed of both ships will decrease
D) Due to the boundary layer the pressure on both ships will increase

Explain your answer please.

Solution:
The right answer is "B"
The two mass will be pulled toward each other due to the Newton law of gravity that has inverse relationship with the distance between the two objects. The lesser the distance the more the gravity.

9 - Question 5 - HP of the escalator - by Kambiz Ehsani - 4/22/2018 - Solved

An escalator must be installed in South Coast Plaza in Orange County California. Design considerations of the escalator are :
1) It moves 30 people in 2 minutes.
2) Each person average weight is 200 pounds
3) Escalator lift is 30 feet
4) Efficiency of the motor or "e" is 0.75

Need to know the horse power of the motor driving the escalator.

Solution:
Delta E = Change in the Potential Energy for all 30 people = 30 * mgh = 30 * 200 * 30 = 180,000 J
Time = t = 2 minutes = 120 seconds
Power (demand) = Pd = Delta E / t = 1,500 lb.ft/sec  or 1,500 / 550 = 2.7 hp -demand
Power (motor) = Pm = Pd / e = 2.7 / 0.75 = 3.6 hp

8- Question 4 - Energy burned in uphill biking - by Kambiz Ehsani - 4/22/2018 - Solved

You are biking uphill with a constant speed of 15 miles per hour. The weight of the bike and you together will be 200 pounds.Assume the slope 5%. How many Kilo Calories will you pedal in 10 minutes? is that the same as Kilo Calories burned by your body? please explain all of your assumptions:

The question was designed by myself as one day I thought, how the apps on my smart phone calculate my Kilo Calories burned :-)

Solution:
Writing the free body diagram of the mass of you and bike as a rigid body on the inclined surface:
f = Friction force = m*g* Sin (Teta)
Power of pedaling = m*g* Sin (Teta) * v = hp = horse power
v = assumed constant velocity
Teta = the angle for the slope
hp = 200 * 5/(10025)^0.5* 15 * 0.44704/0.3048 = 0.4 = 294 watts = 70 cal/sec
Pedaling Power = Pp = 70 cal / sec = in 10 minutes or 600 seconds = 42,000 cal = 42 kcal

This is the pedaling Kilo Calories. The body has an efficiency in converting the food intake energy to exercise energy or useful work. This efficiency is different from person to person. for every 1 Calorie we eat only 0.75 calories turns into useful work. So the efficiency of the body is approximately 25%. So the pedaling calorie and burning calories are not the same. So the burning calories are:

Burned Power = Pb = Pp / 0.75 = 56 Kcal


By the way all the units on the Fitness machines should be expressed as Kcal and it is as we know expressed as Cal.