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When air enters a compressor at pressure P1 and leaves at
Chapter 3, Problem 5E(choose chapter or problem)
When air enters a compressor at pressure \(P_1\) and leaves at pressure \(P_2\), the intermediate pressure is given by \(P_3\sqrt {P_1P_2}\). Assume that \(P_1=10.1 \pm 0.3 \mathrm{\ MPa}\) and \(P_2=20.1 \pm 0.4 \mathrm{\ MPa}\).
a. Estimate \(P_3\), and find the uncertainty in the estimate.
b. Which would provide a greater reduction in the uncertainty in \(P_3\): reducing the uncertainty in \(P_1\) to 0.2 MPa or reducing the uncertainty in \(P_2\) to 0.2 MPa?
Equation Transcription:
Text Transcription:
P_1
P_2
P_3=sqrt{P_1P_2}
P_1=10.1{+/-}0.3 MPa
P_2=20.1{+/-}0.4 MPa
P_3
P_3
P_1
P_2
Questions & Answers
QUESTION:
When air enters a compressor at pressure \(P_1\) and leaves at pressure \(P_2\), the intermediate pressure is given by \(P_3\sqrt {P_1P_2}\). Assume that \(P_1=10.1 \pm 0.3 \mathrm{\ MPa}\) and \(P_2=20.1 \pm 0.4 \mathrm{\ MPa}\).
a. Estimate \(P_3\), and find the uncertainty in the estimate.
b. Which would provide a greater reduction in the uncertainty in \(P_3\): reducing the uncertainty in \(P_1\) to 0.2 MPa or reducing the uncertainty in \(P_2\) to 0.2 MPa?
Equation Transcription:
Text Transcription:
P_1
P_2
P_3=sqrt{P_1P_2}
P_1=10.1{+/-}0.3 MPa
P_2=20.1{+/-}0.4 MPa
P_3
P_3
P_1
P_2
ANSWER:
Solution:
Step1 of 3:
The intermediate pressure in a compressor is given that .Here, and 20.1 Mpa.
We have to find
- The estimate , and the uncertainty in the estimate.
- Which would provide a greater reduction in the uncertainty in : reducing the uncertainty in to 0.2 Mpa or reducing the uncertainty in to 0.2 Mpa.