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When air enters a compressor at pressure P1 and leaves at

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 5E Chapter 3.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 5E

When air enters a compressor at pressure P1 and leaves at pressure P2, the intermediate pressure is given by  Assume that P1 = 10.1 ± 0.3 MPa and P2 = 20.1 ± 0.4 MPa.

a. Estimate P3, and find the uncertainty in the estimate.

b. Which would provide a greater reduction in the uncertainty in P3: reducing the uncertainty in P1 to 0.2 MPa or reducing the uncertainty in P2 to 0.2 MPa?

Step-by-Step Solution:
Step 2 of 3

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.

Step 2 of 3:

Here it is given that the intermediate pressure of a compressor P3= .

 Mpa which means and the uncertainty .       which means  , and the uncertainty .

So the intermediate pressure

                               

                                     =  

                                     =    14.24

And

                       

                                  =    

                                         =    0.5   1.410

                                           

                                         =    0.7053                        

                                   =  

               

                                         =    0.5   0.7088

                                         =    0.3544

So the uncertainty in the estimate is  

                                   

                                 

                                 

                                         

                                           =    

                                           =    0.25 Mpa

Therefore the estimate of the intermediate pressure is (14.24 0.25) Mpa. and the uncertainty in the estimate is 0.25 Mpa.

Step 3 of 3

Chapter 3.4, Problem 5E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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