This HW covers CB chapter 5 or LT chapter 5.

The homework consists of 10 problems for a total of 65 pts.

Please begin your question with the problem number you are asking about.

Cengel & Boles, Ch 5:

5.35 - Adiabatic Steam Nozzle - 5 pts

5.54 - Adiabatic Gas Turbine - 5 pts

5.112 - Steam Flow in a HEX Tube - 5 pts

5.138 - Filling a Balloon with Helium - 10 pts

5.142 - Charging a Cylinder with a Spring-Loaded Piston - 8 pts

Special Problems

WB-1 - Effluent Pressure in a Non-Adiabatic Steam Diffuser - 5 pts

WB-2 - Steady-State, Polytropic Air Compressor - 5 pts

WB-3 - Analysis of a Two-Stage, Adiabatic Turbine - 6 pts

WB-4 - Analysis of an Adiabatic Steam De-Superheater - 8 pts

WB-5 - Waste Heat Steam Generator - 8 pts

## 52 comments:

On WB-3 which two exits are we supposed to find the mass flow rate for? (in reference to the numbers that the diagram gives for the problem)like number 5 and 3/4?

Thanks

So on WB-1 when it says Heat transfer occurs from the steam to the surroundings at a rate of 19.59 Btu/lbm of flowing steam. Is the 19.59 a number that represents Q dot or Q hat? I think Q hat but I am not sure.

Also on WB-1 how do you get m dot without knowing the cross sectional area...?

WB-3 , Anon , 2:05pm

You need to determine the mass flow rate of streams 4 and 5.

WB-1 , Jayson , 7:51pm

You are correct. The value of 19.59 Btu/lbm is really Qhat, but don't forget it is negative b/c of our sign convention !

WB-1 , Jayson , 8:24pm

You don't need to determine mdot. Qhat = Qdot / mdot. So, just divide the 1st Law for open systems by mdot and you should be good to go.

I hope this helps!

if a process is steady, or steadily, does that automatically mean the m(dots) will cancel out? if so, when wont they? only when there is an accumulation of mass in the system?

No Specific Problem Anon , 3:19 pm

No. In a process operating at steady-state, no variable changes with respect to TIME. So mdot does not change as time goes by, but it does not necessarily "cancel out". I am not sure what you mean by cancel out. In a SISO system, mdot,in = mdot,out. I think you need to come and see me during my office hour one day this week to clear this up !

Sorry I could not be more helpful, but I don't think I really understand your question.

5.138

This problem is complicated because there is flow work as the He inflates the balloon because the He must overcome the pressure inside the balloon in order to flow into the balloon. The good news is that this flow work taken into account in the analysis we developed in class today (Monday, 4/18).

But this problem also has moving boundary work that the system does on the surroundings. The restraining force is exerted by the air surrounding the balloon

andby the rubber ballon itself ! The result is that there IS aboundary workterm in the transient form of the 1st Law. I think I left this term out when we worked on this one in class today.The good news is that because the volume of the ballon increases linearly with pressure, Wb is not hard to evaluate. The path is a straight line on the PV Diagram and Wb = INT{P dV} = { (P1+P2)/2 } * (V2-V1).

5.142

This problem requires an iterative or trial-and-error solution. I STRONGLY advise you to use NIST or the TFT Plug-in to solve this problem. Gues T2 values between 200 and 250 degC and get specific volume and specific internal energy values for each T2. Use the transient 1st Law equation to calculate the work output associated with each T2. Pick the T2 value that gives you a work output that is equal to the work done against the spring. I would like you to get T2 to the nearest whole degC. The repetitive calculation of work at the various values of T2 will be easier in Excel than by hand.

On 5-142 I have one equation and two unknowns. From the first law for transient systems I have it in terms of vhat and u2. Which other relationship can I use to help me find the final temperature?

5.142 , Anon , 3:19pm

Take a look at the comment immediately above yours. I posted it at 11:59 am today.

It sounds like you are doing the problem correctly, which is excellent. The other "Eqn" or really the other 2 "Eqns" that you have are the steam tables (either on paper, on NIST or in the TFT plug-in). So, you have 3 unknowns: T2, V2hat and U2hat. You have 3 eqns as well: the first law and both U2hat=fxn(P2,T2) and V2hat=fxn(P2,T2) [these two "eqns" are really steam tables or the high-powered EOSs used to generate the steam tables.

As I said in my previous post, guess a table of T2 values and check to see if the 1st Law equation is an equality (or close enough). When you pick the correct T2 value, the left-hand side of the 1st Law should be equal (or nearly equal) to the right-hand side. I want you to find T2 to the nearest whole degC that makes the 1st Law closest to an equality.

5.112 - hint

I found Q = -19.9 kW and not +19.9 kW. Did anyone else get the result I got ? Watch those kJ (in H) and the J (in Ekinetic).

In problem WB-1, I already get H2 head from the 1st law equation. Since the kinetic energy is negligible, I assume that velocity 1 is approximately the same as velocity 2. Is that right? And how do I proceed from here?

WB-1 , Anon , 4:05pm

The problem statement says that kinetic energy at the outlet is negligible. From this you can conclude that Ek2 ~ 0 kJ/kg or v2 ~0 m/s.

I am not sure what you mean by "H2 head". You need to use the information in the previous paragraph and the 1st Law to determine H2. Then, you can use the steam tables to determine P2 because you know x2 = 1.

I hope this helps!

I think there's a typo in problem WB-2 for V1 dot is supposed to be in ft3/s not in ft3/min

WB-2 , Anon , 5:23 pm

Hmmm. I used 500 ft^3/min in my solution and I don't see any problems. What makes you think it should be ft^3/sec ?

What is the input into excel in place of SI_C when using American Engineering Units in degrees Fahrenheit?

In problem WB-1 how can you determine P2 using X2 = 1 if you do not know T2?

On WB-5 im trying to find the heat transferred by the air to the water, but I appear to be missing the v hat for air when I'm trying to calculate m dot for the

Q - Ws = mdot(dH) equation for air so I can solve for Q which I will then plug into the turbine equation. theres no air tables on NIST or in the book. Does the fact that its a ideal gas help me with this somehow?

General , Jayson , 4:55 pm

You must tell the TFT plug-in what chemical you are using. Common names for this course are: Water, R-134a, Ammonia.

For unit systems, you have 4 choices: SI_C, SI_K, EE_F and EE_R.

I will post a PDF on the course website about how to use the TFT plug-in by the guys who created it.

WB-1 , Jayson , 8:33 pm

You need to solve the 1st Law eqn for H2. Then, you know 2 intensive properties: x2 and H2. So you can interpolate in NIST or the steam tables or use the TFT plug-in to determine P2. The TFT formula would look like:

=TFPROP("Water","EE_F","x",1,"H",####,"P") where H is in Btu/lbm and P is in psia.

WB-5 , Camden , 9:36pm

You need to use the ideal gas EOS to determine Vhat for air.

Apply the 1st law to each individual unit in the process: one 1st Law eqn for the HEX and another for the turbine. Start with the HEX. This will let you determine the water flow rate in streams 1, 2 & 3.

I hope this helps.

Dr. B - 6.16 PM

Oops, sorry, I misread the problem.

Never mind..

5-54

I cant find the v-head of argon at 450C and 1.6MPa when i am calculating the m-dot?

5.54 , Kelvin , 8:10am

Use the IG EOS to determine Vhat for the argon. Just be sure to verify whether this is an accurate method.

How can you verify that a gas is ideal without having A volume amount given? Do you some algebraic manipulation with volumetric flow and mass flow or something?

Thanks

In problem WB-4, why are you referring to T2 and Hsatliq instead of T3 and Hsatvap to plot the graph?

Also in WB-2 I assumed no kinetic and potential energy, that leaves Qdot-Wdot = mdot*(H2-H1). Then with another algebraic manipulation I turned the Qdot and Wdot into Qhat*mdot-W_hat-mdot= mdot*(H2-H1) and then divided by mdot, which gets rid of it. The question is, do I want to do that, and is that a legitimate step?

Jayson , 2:45pm

One way is to ASSUME the Ideal Gas EOS applies and use it to calculate the molar volume. Then, compare this molar volume to 20 L/mol or 5 L/mol (diatomic & noble gases). This is not perfect, but it is MUCH better than just making the IG assumption and never thinking about it again.

I hope this helps.

Disregard my comment made at 2:53 I realize that is not a good approach, I put mdot back in the problem (WB-2) and I solved for it no problem, and I used the plugin to find H1. However there is still H2 Qdot and Wdot. I am thinking maybe for Wdot I could use the area under the polytropic curve but that still leaves H2 and Qdot and I cant figure out what equation to use.

Thanks For Helping by the way. I can not do this alone.

Can we assume WB-2 is adiabatic? Cause if we can my problems are smaller.

WB-4 , Anon , 2:50pm

DOH ! My mistake. Thank you for pointing this out !

I changed the process flow diagram and the stream numbers and forgot to change the hint! All the "T2" references in the hint should be "T3". But the reference in the hint to Hsatliq is correct.

Stream 3 is a subcooled liquid. The lowest P table in the subcooled liquid table in your book is for 5MPa and P3 = 2.5 MPa. As a result, you need to interpolate between Hsatliq at 200C and H(5MPa,T3) to get H3=H(2.5 MPa,T3).

This process is painful using the tables. I suggest you use either the NIST Webbook or the TFT plug-in for Excel.

I hope this helps!

WB-2 , Jayson , 2:53pm

OK, I disregarded this question as you instructed in your next comment.

WB-2 , Jayson , 3:22pm

Yes, it is ok to divide the 1st Law by mdot and write it as: Q_hat - Ws_hat = deltaE_hat.

But the wierd part of this problem is that you do NOT need to write or solve the 1st Law to answer the question ! You already determined mdot. Use th polytropic path eqn to determine D2 and then use the IG EOS to determine T2.

WB-2 , Jayson , 3:37pm

N, you do not need to assume the compressor is adiabatic. Take a look at my previous comment.

Thank you but that is frustrating cause I have been trying to use different variations of the first law for at least an hour. I need to think outside the box more.

For WB-2 When using the polytropic equation P1V1^1.34= Constant, can you use the specific volume or the volume flow rate, or do you need to solve for volume?

WB-2 , Jayson , 4:15

You can use Vdot or Vhat or Vwiggle because they are all proportional to each other in this case.

I don't see any way to calculate plain old volume, V, because this is a flow problem.

Problem 5.35

after writing the first law and neglect all necessary terms, I end up with H2(hat)-H1(hat)+

+mass*(((V2^2)-(V1^2))/2) From table I get H1(hat), but I don't have mass value. in order to find H2

Please help!

Thanks

@Dr.B: 5.112

Yeah, I got -19.938 kW also....

5.35 , Andrei , 6:42pm

You should have reduced the 1st Law to 0 = mdot*(DH^+DEk^)

Then, divide by mdot and it drops out of the problem! Always watch the units !

I hope this helps.

5.35

o.k I understand this, but lets look at the units "delta"H(hat) in kJ/kg and "delta"Ek in (m/s)^2. ...or I have to devide everything by Gc ((kg*m)/N*s^2))

?

wb1

I've got to the point where i found H2(hat) but don't know what table to use in order to find T. I have a quality=1 (100%vapor) but P2 unknown. What table to use to find T2.

My value for H2 is kind of large 5059Btu/lbm

TThank you

5.35

Yes!!!Solved. I figured it out after "playing" with units!

Thank you

Ok thanks Dr. B that helps a lot.

Not sure if your still up Dr. B, but I am having trouble on finding diameter in WB-2. I think I should use a volume equation but I am not sure how volume can help me get diameter, cause the shape of the compressor is funky. Perhaps, the equation Velocity=(1/A)2pi(vr dr)integrated from r to 0?

Hey Jason,

I am working on WB-2 too.

Look, you can find diameterthrough formula: Area=(PI/4)*D^2 ==> D=2*sqrt(Area/Pi)

let me know what answers you get, because my answers doeasn't match with answers on the HW sheet

I'm working on this too, if we dont figure it out, Hes supposed to have an office hour from 8 to 9 am on homework days, just in case you guys didn't know

yes, I will see you guys at 8am

Hey for WB-2 I got .743 in and 630 degrees Fahrenheit. I am working on WB-3 now it is going ok I think...and ya I will see you at 8 haha.

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