Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 11, Problem 11.33P
To determine

(a)

The value of the diameter.

Expert Solution
Check Mark

Answer to Problem 11.33P

The required value of the diameter is 47cm

Explanation of Solution

Given Information:

Fluid Mechanics, Chapter 11, Problem 11.33P , additional homework tip  1

BEPflowrate=2000gal/minDiameter(d)=16inSpeed(n)=1200r/min

Formula used:

η1=η2=γQ1H1P1

Q1n1D13=Q2n2D23

gH1n12D12=gH2n22D22

Calculation:

To solve this problem, we are taking the value of specific weight of the water as γ=9790N/m3.

Now we will find the efficiency;

η1=η2=γQ1H1P1 ;

Put the values in the above equation;

(9790N/m3)(7.57/60m3/s)(24.67m)(48x746W)

0.851

85.1%

Now we will use the scaling laws for BEP flow rate and head;

Q1n1D13=7.57(1200)(0.406)3=Q2n2D23=15.14n2D23

gH1n12D12=(9.81)(24.67)(1200)2(0.406)2=gH2n22D22=(9.81)(54.86)n22D22

Solve for D2 and n2 simultaneously:

D2=47cm

n2=1545r/min.

To determine

(b)

The speed that will deliver a BEP water flow rate of 15.14m3/min and a head of 54.86m.

Expert Solution
Check Mark

Answer to Problem 11.33P

The required value of the speed is 1545r/min

Explanation of Solution

Given information:

Fluid Mechanics, Chapter 11, Problem 11.33P , additional homework tip  2

BEPflowrate=2000gal/minDiameter(d)=16inSpeed(n)=1200r/min

Formula used:

Q1n1D13=Q2n2D23

gH1n12D12=gH2n22D22

Calculation:

Explained in the above part;

Repeat:

Now we will use the scaling laws for BEP flow rate and head;

Q1n1D13=7.57(1200)(0.406)3=Q2n2D23=15.14n2D23

gH1n12D12=(9.81)(24.67)(1200)2(0.406)2=gH2n22D22=(9.81)(54.86)n22D22

Solve for D2 and n2 simultaneously:

D2=47cm

n2=1545r/min.

To determine

(c)

The brake horsepower.

Expert Solution
Check Mark

Answer to Problem 11.33P

The required value of the brake horsepower is 213hp

Explanation of Solution

Given Information:

Fluid Mechanics, Chapter 11, Problem 11.33P , additional homework tip  3

BEPflowrate=2000gal/minDiameter(d)=16inSpeed(n)=1200r/min

Formula used:

P2=γQ2H2η2

Calculation:

We know the formula for the required horse power, i.e.: P2=γQ2H2η2 ;

Put the values in the above equation

P2=γQ2H2η2=(9790)(15.14/60)(54.86)0.8531.59kW/746213hp.

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Chapter 11 Solutions

Fluid Mechanics

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