(a) To determine The resisting torque required to hold the rotor stationary. The rotor spin rate if the resisting torque is reduced to zero at θ = 0 ° . Explanation Write the expression of mass flow rate. m ˙ = ρ Q (I) Here, the density is ρ and the flow rate is Q . Write the expression of outer velocity of water. V out = Q 3 A nozzle (II) Here, the area of the nozzle is A nozzle . Write the expression of required torque by using Moment of moment torque equation. T shaft = m ˙ r out V out cos θ (III) Here, the exit radius of the nozzle is r out and the angle is θ . Substitute Q 3 A nozzle for V out and ρ Q for m ˙ in Equation (III). T shaft = ( ρ Q ) r out ( Q 3 A nozzle ) cos θ = ρ Q 2 r out cos θ 3 A nozzle (IV) Write the expression of rotor velocity at outlet. U out = r out ω (V) Here, the angular velocity is ω . Write the expression of shaft torque by using velocity. T shaft = m ˙ r out ( V out cos θ − U out ) (VI) Substitute r out ω for U out , Q 3 A nozzle for V out and ρ Q for m ˙ in Equation (VI). T shaft = ( ρ Q ) r out { ( Q 3 A nozzle ) cos θ − r out ω } (VII) Conclusion: Substitute 998 kg / m 3 for ρ , 5 Ltr / s for Q , 0.5 m for r out , 0 ° for θ and 18 mm 2 for A nozzle in Equation (IV). T shaft = ( 998 kg / m 3 ) × ( 5 Ltr / s ) 2 × ( 0 (b) To determine The resisting torque required to hold the rotor stationary. The rotor spin rate if the resisting torque is reduced to zero at θ = 30 ° . (c) To determine The resisting torque required to hold the rotor stationary. The rotor spin rate if the resisting torque is reduced to zero at θ = 60 ° .

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Chapter 5.2, Problem 83P

(a)

To determine

The resisting torque required to hold the rotor stationary.

The rotor spin rate if the resisting torque is reduced to zero at θ=0°.

(b)

To determine

The resisting torque required to hold the rotor stationary.

The rotor spin rate if the resisting torque is reduced to zero at θ=30°.

(c)

To determine

The resisting torque required to hold the rotor stationary.

The rotor spin rate if the resisting torque is reduced to zero at θ=60°.

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Chapter 5.2, Problem 82P

Chapter 5.2, Problem 84P

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Chapter 5 Solutions

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

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The resisting torque required to hold the rotor stationary. The rotor spin rate if the resisting torque is reduced to zero at θ = 0 ° .

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The resisting torque required to hold the rotor stationary. The rotor spin rate if the resisting torque is reduced to zero at θ=0°.

The resisting torque required to hold the rotor stationary. The rotor spin rate if the resisting torque is reduced to zero at θ=30°.

The resisting torque required to hold the rotor stationary. The rotor spin rate if the resisting torque is reduced to zero at θ=60°.

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Chapter 5 Solutions

The resisting torque required to hold the rotor stationary.

The rotor spin rate if the resisting torque is reduced to zero at θ=0°.

The resisting torque required to hold the rotor stationary.

The rotor spin rate if the resisting torque is reduced to zero at θ=30°.

The resisting torque required to hold the rotor stationary.

The rotor spin rate if the resisting torque is reduced to zero at θ=60°.