Water flows steadily from a large open reservoir through a narrow horizontal pipe of…

PHYSICS · Multi-part · CBSE · Physics · Mechanical Properties of Fluids · Mechanical Properties of Fluids

Problem

Water flows steadily from a large open reservoir through a narrow horizontal pipe of cross-sectional area

2.0\times10^{-4}\,\text{m}^2

. Just before the pipe terminates, the speed of the water is measured to be

4.2\,\text{m/s}

. The pipe ends at a vertical piston that moves so slowly that its speed can be neglected. The piston’s cross-sectional area is

0.012\,\text{m}^2

and its outward face is exposed to atmospheric air. The pipe inlet is 6.0 m below the reservoir surface. Assume

\rho_{\text{water}} = 1000\,\text{kg/m}^3

and

g = 9.8\,\text{m/s}^2

. Neglect energy losses in the pipe. (a) Determine the gauge pressure of the water immediately behind the piston. (b) Calculate the magnitude of the force exerted by the water on the piston. (c) Engineers wish to redesign the system so that the force on the piston is limited to

300\,\text{N}

while the flow speed in the pipe remains the same. Calculate the piston cross-sectional area required to achieve this objective.

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