A small circular hole 6.00 mm in diameter is cut in the side of a large water tank, 14.0 m below

step 1 Okay, so in this problem we have a water tank, so let's try to draw the tank in here. The tank i

A small circular hole 6.00 mm in diameter is cut in the side...

A small circular hole 6.00 $\mathrm{mm}$ in diameter is cut in the side of a large water tank, 14.0 $\mathrm{m}$ below the water level in the tank. The top of the tank is open to the air. Find the speed at which the water shoots out of the tank.

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Key Concepts

Fluid Statics and Hydrostatic Pressure

Fluid statics involves the study of fluids at rest, and a key concept is hydrostatic pressure. Hydrostatic pressure increases with depth according to the product of fluid density, gravitational acceleration, and depth. This pressure difference between points in a fluid is what drives the fluid to accelerate out of an orifice when exposed to atmospheric pressure.

Bernoulli's Principle

Bernoulli's principle relates the pressure, velocity, and height of a fluid along a streamline. It explains how an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or potential energy. This conservation of energy in fluid flow underpins the derivation of Torricelli's law.

Torricelli's Law

Torricelli's law states that the speed of a fluid flowing out of an opening under the influence of gravity is equal to the square root of twice the product of gravitational acceleration and the height of the fluid above the opening (v = ?(2gh)). This concept, derived from energy conservation, is central to calculating the exit velocity of fluids in systems where gravity acts as the driving force.

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