Steam Quality Solution Assistance: X = 0.9959 - 0.000442T_E - ln[(P_S+6.8) 0.3218...]

[cl10Greg]

Hello everyone,

First poster here. I have a problem that I've been having an issue figuring out how they get the final answer.

I am using this equation:

. . . . .\(\displaystyle X\, =\, 0.9959\, -\, 0.000442T_E\, -\, \ln\big[\left(P_S\, +\, 6.8\right)\, 0.03218\, \left(P_S\, +\, 374\right)^{-0.0001581TE}\big]\qquad \left(\mbox{Eqn. 4}\right)\)

They give an example that if you use Te = 250, Ps = 200, and you should get a result of 0.9649. I tried to work this a few times by the following:

• First I tried to just plug it all into Wolfram Alpha and it gave me -0.758854
• Based on that wrong answer, I tried to figure out the value that needed to be logged to get the wrong answer and found out that it should be 0.92358
• Now with that value I tried to work it backwards to say what value of Te and Ps needs to be to make that happen, they didn't equal 250, 200 like it should be
• I also tried to see that maybe it was a different log base for some reason and found the log base that it would require to make that number work for Ps and Te but it didn't work if I put in other numbers and tried to solve.

Any thoughts on what's going on or what I am missing to solve this?

Thanks,
Greg

 

[Dr.Peterson]

Hello everyone,

First poster here. I have a problem that I've been having an issue figuring out how they get the final answer.

I am using this equation (image):

View attachment 9708

They give an example that if you use Te = 250, Ps = 200, and you should get a result of 0.9649. I tried to work this a few times by the following:

• First I tried to just plug it all into Wolfram Alpha and it gave me -0.758854
• Based on that wrong answer, I tried to figure out the value that needed to be logged to get the wrong answer and found out that it should be 0.92358
• Now with that value I tried to work it backwards to say what value of Te and Ps needs to be to make that happen, they didn't equal 250, 200 like it should be
• I also tried to see that maybe it was a different log base for some reason and found the log base that it would require to make that number work for Ps and Te but it didn't work if I put in other numbers and tried to solve.

Any thoughts on what's going on or what I am missing to solve this?

Thanks,
Greg

The equation is

X = 0.9959 - 0.000442T_E - ln[(P_s + 6.8)0.03218(P_s + 374)^(-0.0001581 T_E)]
​

I got the same value you got; but I realized the expression looks very odd, with 0.03218 stuck between two other factors, and I wondered if that was meant to be an exponent:

X = 0.9959 - 0.000442*T_E - ln[(P_s + 6.8)^0.03218 * (P_s + 374)^(-0.0001581*T_E)]
​

This gave the correct result:

0.9959 - 0.000442*250 - ln[(200 + 6.8)^0.03218 * (200 + 374)^(-0.0001581*250)] = 0.9649118929395599
​

So there was a typo in the equation.

 

[cl10Greg]

Ah! Thank you so much. That did seem odd that it was just floating there. Good call and appreciate the help.

Thanks,
Greg