A cylindrical container of cross-sectional area holds two immiscible liquids in…

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

Problem

A cylindrical container of cross-sectional area 3.0×10−3 m23.0\times10^{-3}\,\text{m}^2 holds two immiscible liquids in static equilibrium. A 0.12 m0.12\,\text{m} layer of motor oil (density 8.0×102 kg m−38.0\times10^{2}\,\text{kg}\,\text{m}^{-3}) floats on top of a 0.25 m0.25\,\text{m} layer of water (density 1.00×103 kg m−31.00\times10^{3}\,\text{kg}\,\text{m}^{-3}). The oil is exposed to atmospheric pressure, Patm=1.01×105 PaP_{\text{atm}}=1.01\times10^{5}\,\text{Pa}. (a) Calculate the gauge pressure at the oil–water interface. (b) Determine the absolute pressure at the bottom of the water layer. (c) The container has a small drain valve flush with the bottom surface. When the valve is opened, water begins to flow out horizontally. Assuming the water exits the valve at the bottom surface level and neglecting viscosity, calculate the speed of the water as it leaves the valve.

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