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# A large tank filled with water has two holes in the bottom, one with twice the radius of the other. In steady flow the speed of water leaving the larger hole is _______________the speed of the water leaving the smaller.(A) twice(B) four times(C) half(D) the same as

Last updated date: 21st Apr 2024
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Hint: We know that Bernoulli's theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar. The Bernoulli equation is an important expression relating pressure, height and velocity of a fluid at one point along its flow. Because the Bernoulli equation is equal to a constant at all points along a streamline, we can equate two points on a streamline.

Velocity of water surface $_{1}=0$
From Bernoulli equation $\mathrm{P}+\dfrac{\rho \mathrm{v}^{2}}{2}+\rho \mathrm{gh}=\mathrm{constant}$
$\mathrm{P}_{\mathrm{atm}}+\dfrac{\rho \mathrm{v}_{1}^{2}}{2}+\rho \mathrm{gh}_{1}=\mathrm{P}_{\mathrm{atm}}+\dfrac{\rho \mathrm{v}_{2}^{2}}{2}+\rho \mathrm{gh}_{2}$
$\dfrac{\rho \mathrm{v}_{2}^{2}}{2}=\rho \mathrm{g}\left(\mathrm{h}_{1}-\mathrm{h}_{2}\right)$
$\mathrm{v}_{2}=\sqrt{2 \mathrm{g}\left(\mathrm{h}_{1}-\mathrm{h}_{2}\right)}$
Velocity of water is $\sqrt{2 \mathrm{g}\left(\mathrm{h}_{1}-\mathrm{h}_{2}\right)}$