Concept explainers
The nozzle shown discharges a stream of water at the rate of 200 gal/min. Knowing that at both B and C the stream of water moves with velocity of magnitude 100 ft/s, and neglecting the weight of the vane, determine the force-couple system that must be applied at A to hold the vane in place
The force couple system that must be applied at A to hold the vane in plane.
Answer to Problem 14.112RP
The reaction force at A is
Explanation of Solution
Given:
Rate of discharge of water is
Magnitude of velocity of water is
Concept used:
Write the expression for mass flow rate of water.
Here,
Draw the impulse moment diagram for the vane as shown below:
Consider
Simplify the above expression for
Here,
Consider the
Simplify the above expression.
Write the expression for the magnitude of reaction force at
Here,
Write the expression for the direction of reaction at A.
Write the expression for momentum equilibrium at point A.
Simplify the above expression for
Here,
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
The reaction force at A is
Conclusion:
Thus, the reaction force at A is
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Chapter 14 Solutions
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