A sturdy rectangular tank completely filled with water is sealed with a rigid lid

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

Problem

A sturdy rectangular tank completely filled with water is sealed with a rigid lid. Compressed air above the water surface maintains the absolute pressure of the air–water interface at

1.3\,\text{atm}

. Outside the tank, the atmospheric pressure is

1.0\,\text{atm}

. A very small circular opening in the flat bottom of the tank allows water to flow out into the surrounding air. The vertical distance between the water surface inside the tank and the opening is 2.0 m. Use

1.0\,\text{atm}=1.01\times10^{5}\,\text{Pa}

\rho_{w}=1.0\times10^{3}\,\text{kg}\,\text{m}^{-3}

, and

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

. (a) Determine the gauge pressure (relative to the outside atmosphere) acting on the water surface inside the tank. (b) Calculate the speed with which water exits the opening. (c) Compute the kinetic energy per unit mass of the water in the emerging jet and interpret its physical meaning in the context of the situation.

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