A tank is filled with water of density 1 g cm - 3 and oil of density 0 .9 g cm - 3 . The height of the water layer is 100 cm and of the oil layer is 400 cm . If g = 980 cm s - 2 , then the velocity of

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A tank is filled with water of density 1 g cm - 3 and oil of density 0 .9 g cm - 3 . The height of the water layer is 100 cm and of the oil layer is 400 cm . If g = 980 cm s - 2 , then the velocity of efflux from an opening in the bottom of the tank is

TestHub · Accepted Answer

Pressures at the bottom of the tank must be equal to the pressures due to water of height $h .$

If $d_{w} a n d d_{0}$ be the densities of water and oil respectively, Pressure at the bottom of the tank

$= h_{w} d_{w} g + h_{0} d_{0} g$

If this pressure be equivalent to pressure due to water of height $h .$

Then, $h d_{w} g = h_{w} d_{w} g + h_{0} d_{0} g$

$h = h_{w} + \frac{h_{0} d_{0}}{d_{w}} = 100 + \frac{400 \times 0.9}{1}$

$= 100 + 360 = 460$

According to Torricelli's theorem

$v = \sqrt{2 g h} = \sqrt{2 \times 980 \times 460}$

$= \sqrt{920 \times 980} cm s^{- 1}$

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