Λtank, which is opcn al the top, contains a liquid up to a height H . Λsmall hole is made in the

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Λtank, which is opcn al the top, contains a liquid up to a...

$\Lambda$ tank, which is opcn al the top, contains a liquid up to a height $H . \Lambda$ small hole is made in the side of the tank al a distance $y$ below the liquid surface. The liquid emcrging from he hole, lands al a distance $x$ from the Lank. Then (a) if $y$ is incrcased from zero to $H, x$ will first increase and then decrease (b) $x$ is maximum for $y=H / 2$ (c) the maximum valuc of $x$ is $H$ (d) the maximum valuc of $x$ will depend on the densily of the liquid

$\Lambda$ tank, which is opcn al the top, contains a liquid up to a height $H . \Lambda$ small hole is made in the side of the tank al a distance $y$ below the liquid surface. The liquid emcrging from he hole, lands al a distance $x$ from the Lank. Then
(a) if $y$ is incrcased from zero to $H, x$ will first increase and then decrease
(b) $x$ is maximum for $y=H / 2$
(c) the maximum valuc of $x$ is $H$
(d) the maximum valuc of $x$ will depend on the densily of the liquid

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Key Concepts

Torricelli's Law

This principle states that the speed of a fluid flowing out of an orifice under gravity is proportional to the square root of the vertical distance from the free surface to the hole. It is derived from energy conservation and is fundamental in determining the exit velocity of the liquid.

Projectile Motion

Once the fluid exits the hole, it follows a parabolic trajectory under the influence of gravity. Analyzing its horizontal distance requires applying the equations of projectile motion, which relate the initial horizontal velocity (obtained from Torricelli's law) to the time of flight and gravitational acceleration.

Optimization of Projectile Range

Determining the maximum landing distance involves finding the optimal position of the orifice relative to the liquid surface. This requires setting up the function for range based on exit velocity and height and using calculus to optimize it with respect to the distance from the free surface.

Fluid Statics

This area of study explains how pressure varies with depth in a fluid at rest. Understanding the pressure difference between the surface and the hole is crucial for applying Torricelli's law, although the density of the liquid ultimately cancels out in the speed calculation for an ideal fluid.

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