Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 11, Problem 11.85P
To determine

(a)

Determine the type of turbine in the prototype.

Expert Solution
Check Mark

Answer to Problem 11.85P

The type of turbine in the prototype is propeller turbine.

Explanation of Solution

Given Information:

Head, Hp=45ft

Speed of turbine, np=360r/min

Power, Pp=4000bhp

=2200000ft.lbf/s

Prototype diameter, Dp=7ft

Model diameter, Dm=1ft

Prototype

Speed of turbine, np=360r/min

Power,

Pp=4000bhp

=2200000ft.lbf/s

Specific speed,

Nsp=np(rpm)Pp(bhp)[Hp(ft)]54

Here, Hp=45ft

Nsp=36040004554

Nsp=195

Therefore, from specific speed range table, the type of turbine in the prototype is propeller turbine

Conclusion:

The type of turbine in the prototype is propeller turbine.

To determine

(b)

Determine the appropriate head for the model test.

Expert Solution
Check Mark

Answer to Problem 11.85P

The appropriate head for the model test is Hm=9.87ft.

Explanation of Solution

Given Information:

Head, Hp=45ft

Speed of turbine, np=360r/min

Power, Pp=4000bhp

=2200000ft.lbf/s

Prototype diameter, Dp=7ft

Model diameter, Dm=1ft

Model head is given by,

gHpnp2Dp2=gHmnm2Dm2

Here, model turbine speed, nm=1180r/min

Hm=Hpnm2Dm2np2Dp2

=45×11802×123602×72

Hm=9.87ft

Conclusion:

The appropriate head for the model test is Hm=9.87ft.

To determine

(c)

Determine the appropriate flow rate for the model test.

Expert Solution
Check Mark

Answer to Problem 11.85P

The appropriate flow rate for the model test is Qm=8.5ft3/s.

Explanation of Solution

Given Information:

Head, Hp=45ft

Speed of turbine, np=360r/min

Power, Pp=4000bhp

=2200000ft.lbf/s

Prototype diameter, Dp=7ft

Model diameter, Dm=1ft

Prototype flow rate,

Qp=PpηpρgHp

Here, efficiency, η=0.88

=22000000.88×1.94×32.2×45

Qp=889.3ft3/s

Model flow rate is calculated using the relation below,

QpnpDp3=QmnmDm3

Qm=QpnmDm3npDp3

=889.3×1180×13360×73

Qm=8.5ft3/s

Conclusion:

The appropriate flow rate for the model test is Qm=8.5ft3/s.

To determine

(d)

Estimate the power expected to be delivered by the turbine model.

Expert Solution
Check Mark

Answer to Problem 11.85P

The turbine model delivers Pm=8.38hp of power.

Explanation of Solution

Given Information:

Head, Hp=45ft

Speed of turbine, np=360r/min

Power, Pp=4000bhp

=2200000ft.lbf/s

Prototype diameter, Dp=7ft

Model diameter, Dm=1ft

Power delivered by model is calculated by the below relation,

Pm=ηmQmρgHm

=0.88×8.5×1.94×32.2×9.87

=4611.2ft.lbf/s

Pm=8.38hp

Conclusion:

The turbine model delivers Pm=8.38hp of power

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Chapter 11 Solutions

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