Isentropic efficiency of a pump

[jdawg]

Homework Statement

Find the isentropic efficiency of the pump: eff_pump=(h_4s-h₃)/(h₄-h₃)

state 3: p₃=1.5 bar, h₃=467.11, x₃=0, v₃=1.0528/1000 m³/kg ,s₃=1.4336 kJ/kg*K, T₃=111.4 deg C

state 4: p₄=60 bar, h₄=474.14, compressed liquid
state 4s: p₄=60 bar, s₃=s_4s

The values in red are the ones I wasn't given, I looked them up in the tables.
How do I find the h4s value?? I tried going to the compressed liquid tables and looking up the enthalpy at 60 bar, but my tables only have 50 bar and 75 bar. So am I supposed to interpolate between those two tables?

Do I need to find the temperatures at states 3 and 4 before I start trying to interpolate? I'm pretty lost on this problem.

Homework Equations

The Attempt at a Solution

 

[SteamKing]

Homework Statement

Find the isentropic efficiency of the pump: eff_pump=(h_4s-h₃)/(h₄-h₃)

state 3: p₃=1.5 bar, h₃=467.11, x₃=0, v₃=1.0528/1000 m³/kg ,s₃=1.4336 kJ/kg*K, T₃=111.4 deg C

state 4: p₄=60 bar, h₄=474.14, compressed liquid
state 4s: p₄=60 bar, s₃=s_4s

The values in red are the ones I wasn't given, I looked them up in the tables.
How do I find the h4s value?? I tried going to the compressed liquid tables and looking up the enthalpy at 60 bar, but my tables only have 50 bar and 75 bar. So am I supposed to interpolate between those two tables?

Do I need to find the temperatures at states 3 and 4 before I start trying to interpolate? I'm pretty lost on this problem.

Homework Equations

The Attempt at a Solution

25 bar sounds like a big step between tabular values, even for compressed liquid. I would recommend you get a better table to use for the values of compressed liquid at 60 bar.

The NIST publishes some good tables on-line for this very purpose:

http://www.nist.gov/srd/upload/NISTIR5078-Tab3.pdf

Try this table and see if it helps. If you have any further questions, please post them.

 

[jdawg]

That table is a lot better! So s₃=s_4s=1.4336 kJ/kg*K. So I went and I looked at the 6MPa table and the lowest entropy value is 6.0703. I thought I could just find the entropy value of 1.4336 and find the corresponding enthalpy in that pressure table. Did I maybe look up the entropy at state 3 incorrectly?

 

[SteamKing]

That table is a lot better! So s₃=s_4s=1.4336 kJ/kg*K. So I went and I looked at the 6MPa table and the lowest entropy value is 6.0703. I thought I could just find the entropy value of 1.4336 and find the corresponding enthalpy in that pressure table. Did I maybe look up the entropy at state 3 incorrectly?

You're looking at the wrong page. Go back to the previous page, and you'll find lower entropy values for compressed liquid at P = 6.0 MPa.

 

[jdawg]

Oh ok! So I tried to interpolate between s1=1.4139 h1=465.68 and s2=1.4686 and h2=486.77
I found h_4s=458.1

I plugged all my values into the isentropic efficiency formula and wound up with a negative percentage... Did I maybe interpolate incorrectly?

 

[SteamKing]

Oh ok! So I tried to interpolate between s1=1.4139 h1=465.68 and s2=1.4686 and h2=486.77
I found h_4s=458.1

I plugged all my values into the isentropic efficiency formula and wound up with a negative percentage... Did I maybe interpolate incorrectly?

Yes, you messed up. h = 458.1 is less than h = 465.68. The correct value for h is going to be between 465.68 and 486.77.

 

[jdawg]

Hmm... What you said makes total sense. I keep getting 458.1 for my h_4s value though.

y=y1+(x1-x)[(y2-y1)/(x2-x1)]
letting enthalpy=y and entropy=x
h_4s=465.68+(1.4139-1.4336)[(486.77-465.68)/(1.4686-1.4139)]

I'm almost positive I'm using all the correct values...

 

[jdawg]

Haha oops... I think it was my formula, let me see if that fixes it.

 

[jdawg]

That was it! Thanks so much for your help!