When air enters a compressor at pressure P1 and leaves at

Chapter 3, Problem 5E

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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

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

  1. The estimate , and the uncertainty in the estimate.
  2. 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.

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