Concept explainers
Indiana Jones needs So ascend a 10-m-high building. There is a large hose filled with pressurized water hanging down from the building top. He builds a square platform and mounts four 4-cm-diameter nozzles pointing down at each corner. By connecting hose branches, a water jet with I Sni s velocity can be produced from each nozzle. Jones, the platform, and the nozzles have a combined mass of 150 kg. Determine (a) the minimum water jet velocity needed to raise the system. (b) how long it takes for the system to rise 10 m when the water jet velocity is 18 m/s and the velocity of the platform at that moment, and (c) how much higher will the momentum raise Jones if he shuts off the water at the moment the platform reaches 10 in above the ground. How much time does he have to jump from the platform to the roof?
Answers: (a) 17.1 m/s. (b) 4.37 s, 4.57 m/s. (C) 1.07 m, 0.933 S
(a)
The minimum velocity needed to raise the platform.
Answer to Problem 78P
The minimum velocity of the water jet is
Explanation of Solution
Given Information:
The combined mass of the system is
Write the expression to calculate the total weight of the platform.
Here, the combined mass is
Write the moment equation.
Here, the mass flow rate at outlet is
Write the expression for the mass flow rate from the four nozzles.
Here, the density of the fluid is
Write the expression to calculate the area.
Here, the diameter of the nozzles is
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
The minimum velocity of the water jet is
(b)
The time taken by the system to rise
Answer to Problem 78P
The time taken to cover a distance of
The velocity at that moment is
Explanation of Solution
Write the moment equation in the vertical direction.
Here, the vertical reaction on the platform is
Write the expression for vertical reaction force.
Here, the acceleration of the system is
Write the expression of third law of motion.
Here, the distance travelled is
Write the expression for first equation of motion.
Here, the final velocity is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The time taken to cover a distance of
(c)
The momentum raised.
The time taken to jump on the roof.
Answer to Problem 78P
The momentum raised is
The time for getting off the platform is
Explanation of Solution
Write the expression for momentum rise.
Here, the time taken to reach the ground is
Write the expression for velocity when platform is descending.
Write the expression for time taken to jump off the platform.
Calculation:
Substitute
Substitute
Substitute
Conclusion:
The momentum raised is
The time for getting off the platform is
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Chapter 6 Solutions
Fluid Mechanics: Fundamentals and Applications
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