EBK FLUID MECHANICS
EBK FLUID MECHANICS
2nd Edition
ISBN: 9780134626055
Author: HIBBELER
Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)
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Chapter 14, Problem
To determine

The initial blade angle and the relative velocity of the water flows onto the blades of the impeller.

Expert Solution & Answer
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Explanation of Solution

Given:

Mean radius (rm) is 75mm.

Discharge (Q) is 0.095m3/s.

Angular speed of the impeller (ω) is 80rad/s.

Calculation:

Calculate the velocity at the midpoint of the impeller (U).

  U=rmω=(75mm)(80rad/s)=(75mm×1m1,000mm)(80rad/s)=6m/s

Calculate the axial velocity of the water through the impeller (Va).

  Va=QA=0.095m3/sπ[(0.1m)2(0.05m)2]=4.0319m/s

Draw the kinematic diagram of the water at the lead of the blade as shown in Figure (I).

EBK FLUID MECHANICS, Chapter 14, Problem 1P

Calculate the initial blade angle (β1).

  tanβ1=VaU=4.0319m/s6m/s

  β1=33.9°

Thus, the initial blade angle is 33.9°.

Calculate the relative velocity of the water (Vrel)1.

  cosβ1=U(Vrel)1cos(22.6°)=6m/s(Vrel)1(Vrel)1=7.23m/s

Thus, the relative velocity of the water flows on to the blades of the impeller is 7.23m/s.

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