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A 7-cm diameter vertical water jet is injected upwards by

Chapter 6, Problem 80P

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QUESTION:

A 7-cm diameter vertical water jet is injected upwards by a nozzle at a speed of 15 m/s. Determine the maximum weight of a flat plate that can be supported by this water jet at a height of 2 m from the nozzle.

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QUESTION:

A 7-cm diameter vertical water jet is injected upwards by a nozzle at a speed of 15 m/s. Determine the maximum weight of a flat plate that can be supported by this water jet at a height of 2 m from the nozzle.

ANSWER:

Step 1 of 3

Find the time to reach a height of 2m from the nozzle using the equation,

\(s = ut - \frac{1}{2}g{t^2}\)

Here, the initial velocity of the jet is u, the height from the nozzle is h, and acceleration due to gravity is g.

Substitute 15 m/s for u, 9.81 for g, and 2 m for s in the above expression, and we get,

\(2 = 15t - \frac{1}{2}9.81{t^2}\)

\(4.9{t^2} - 15t + 2 = 0\)

\(t = 0.139\;{\rm{s,2}}{\rm{.92}}\;{\rm{s}}\)

Find the velocity at a height 2 m from the nozzle using the following equation:

\(v = u – gt\)

Substitute 15 m/s for u and 9.81 for g in the above expression, and we get,

\(v = 15 - 9.81\left( {0.139} \right)\)

\(v = 13.63\;{\rm{m/s}}\)

Find the velocity at height 2 m from the nozzle using 2.92 s for t.

\(v = u – gt\)

Substitute 15 m/s for u and 9.81 for g in the above expression, and we get,

\(v = 15 - 9.81\left( {2.92} \right)\)

\(v =  - 13.645\;{\rm{m/s}}\)

Thus, it is confirmed that 2.92 s for t is not to be considered.

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