A museum wishes to install a steady fountain in which the water jet continually…

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

Problem

A museum wishes to install a steady fountain in which the water jet continually reaches a height

H

above the nozzle. Water is supplied to the storage tank at a constant volumetric rate

Q_{\text{in}}

by an external pump. The tank has a uniform cross-sectional area

A_{t}

and the nozzle is located at the bottom of the tank. After a short transient, the water level in the tank stabilises, so the depth of water above the nozzle remains constant at

H

while the fountain is operating. (a) Derive an algebraic expression for the radius

r

of the circular nozzle in terms of

Q_{\text{in}}

A_{t}

g

, and

H

that will maintain the steady operating condition described. (b) Evaluate your expression for

Q_{\text{in}} = 6.0\times10^{-4}\,\text{m}^{3}\,\text{s}^{-1}

A_{t} = 0.60\,\text{m}^{2}

, and

H = 1.8\,\text{m}

. Express the radius in millimetres to an appropriate number of significant figures.

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