The volume of a liquid flowing per sec out of an orifice at...

The volume of a liquid flowing per sec out of an orifice at the bottom of a tank does not depend upon
(A) the height of the liquid above the orifice.
(B) the acceleration due to gravity.
(C) the density of the liquid.
(D) the area of the orifice.

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Key Concepts

Torricelli’s Law

This principle states that the speed of efflux of a fluid from an orifice under gravity is given by the square root of twice the product of the gravitational acceleration and the height of the fluid above the orifice. It is fundamental in determining the exit velocity of the liquid and highlights that factors like density do not influence this velocity in ideal conditions.

Volume Flow Rate

The volume flow rate is the product of the cross-sectional area of the orifice and the velocity of the liquid as it exits. According to the relationship derived from Torricelli’s law, while the flow rate depends on the area of the orifice and the square root of the product of gravitational acceleration and height, it is independent of the density of the liquid.

Hydrostatic Pressure and Its Implications

Hydrostatic pressure, which is proportional to the product of fluid density, gravitational acceleration, and the height of the fluid column, drives the flow. However, when deriving the exit velocity using Torricelli’s law, the density term cancels out, indicating that the liquid’s density does not affect the velocity or the volumetric flow rate in ideal fluid flow scenarios.

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