Concept explainers
Water enters vertically and steadily at a rate of 10 Ls into the sprinkler shown in Fig. P6-69. Both water jets have a diameter of 1.2 cm. Disregarding any frictional effects, determine (a) the rotational speed of the sprinkler in rpm and (b) the torque required to prevent the sprinkler from rotating.
(a)
The rotational speed of sprinkler.
Answer to Problem 69P
The rotational speed of sprinkler is
Explanation of Solution
Given information:
The volume flow rate is
Write the expression for mass flow rate entering the sprinkler.
Here, density of water is
Write the expression for volume flow rate from each nozzle.
Write the expression for jet area.
Here, diameter is
Write expression for velocity of water jet,the diameter of both nozzle are equal.
Here, volume flow rate from each jet is
Write the expression for angular momentum equation for the sprinkler.
Here, distance of nozzle from sprinkler centre is
Substitute,
Here, angle of sprinkler with vertical is
Write the expression for relative velocity of jet with respect to nozzle.
Here, vertical component of jet velocity is
Substitute
Substitute 0 for
Write the expression for angular velocity of sprinkler.
Here, length of rod is
Write the expression for angular velocity of sprinkler in rpm.
Calculation:
Refer to table "Properties of saturated water" to obtain the density of water as
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The rotational speed of sprinkler is
(b)
The torque required to prevent the rotation of sprinkler.
Answer to Problem 69P
The torque required to prevent the rotation of sprinkler is
Explanation of Solution
Given information:
The distance of nozzle from sprinkler centre is
Write the expression for torque to prevent rotation.
Here, distance from sprinkler centre to nozzle is
Calculation:
Substitute
Conclusion:
The torque required to prevent the rotation of sprinkler is
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Chapter 6 Solutions
Fluid Mechanics: Fundamentals and Applications
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