A liquid having area of free surface ' A^' has an orifice at a depth ^' h^' with an area a^', be

step 1 A liquid having area of free surface A prime has an orifice at the depth of H with an area small

A liquid having area of free surface ' A^' has an orifice at...

A liquid having area of free surface ' $A^{\prime}$ has an orifice at a depth $^{\prime} h^{\prime}$ with an area $a^{\prime}$, below the liquid surface, then the velocity $v$ of flow through the orifice is : (a) $v=\sqrt{2 g h}$ (b) $v=\sqrt{2 g h} \sqrt{\frac{A^{2}}{A^{2}-a^{2}}}$ (c) $v=\sqrt{2 g h} \sqrt{\frac{A}{A-a}}$ (d) $v=\sqrt{2 g h} \sqrt{\frac{1^{2}-a^{2}}{A^{2}}}$

A liquid having area of free surface ' $A^{\prime}$ has an orifice at a depth $^{\prime} h^{\prime}$ with an area $a^{\prime}$, below the liquid surface, then the velocity $v$ of flow through the orifice is :
(a) $v=\sqrt{2 g h}$
(b) $v=\sqrt{2 g h} \sqrt{\frac{A^{2}}{A^{2}-a^{2}}}$
(c) $v=\sqrt{2 g h} \sqrt{\frac{A}{A-a}}$
(d) $v=\sqrt{2 g h} \sqrt{\frac{1^{2}-a^{2}}{A^{2}}}$

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Key Concepts

Finite Reservoir Effects

When the container's free surface area is not much larger than the area of the outflow orifice, the movement of the free surface contributes to the overall energy balance. This requires adjustments or correction factors in the basic efflux speed obtained from Torricelli's law, accounting for the dynamic behavior of the free surface.

Continuity Equation

The continuity equation expresses the conservation of mass in fluid dynamics, stating that the mass flow rate must remain constant along a streamline. It relates the cross-sectional areas of different sections of the flow to the velocities of the fluid, ensuring the overall fluid mass is conserved.

Bernoulli's Principle

Bernoulli's principle relates pressure, velocity, and height along a streamline in a steady, incompressible flow. It is used to deduce energy conservation in flowing fluids, leading to the derivation of fluid speed from differences in elevation and pressure.

Torricelli's Law

This fundamental concept in fluid mechanics states that the speed at which a fluid exits an orifice under the influence of gravity is given by the square root of twice the product of gravitational acceleration and the vertical distance (head) between the free surface and the orifice. It is derived using energy conservation for an incompressible, non-viscous fluid.

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