A siphon is used to drain water from a tank as illustrated in Figure P 14.50 . Assume steady flo

step 1 We are going to use the Bernolis equation over here where at the water surface we can have p1 pl

A siphon is used to drain water from a tank as illustrated...

A siphon is used to drain water from a tank as illustrated in Figure $\mathrm{P} 14.50 .$ Assume steady flow without friction. (a) If $h=1.00 \mathrm{m}$ , find the speed of outflow at the end of the siphon. (b) What If? What is the limitation on the height of the top of the siphon above the end of the siphon? Note: For the flow of the liquid to be continuous, its pressure must not drop below its vapor pressure. Assume the water is at $20.0^{\circ} \mathrm{C},$ at which the vapor pressure is 2.3 $\mathrm{kPa}$ .

Key Concepts

Siphon Operation

The siphon is a device that uses gravity and atmospheric pressure differences to transfer liquid from one level to a lower level, even when the source is above the exit point. Understanding how the siphon works involves applying energy conservation and recognizing that fluid will continue to flow as long as the pressure at the highest point does not fall below the vapor pressure.

Vapor Pressure and Cavitation

Vapor pressure is the pressure at which a liquid begins to vaporize. In the context of a siphon, the fluid must maintain a pressure above its vapor pressure to remain in liquid form and avoid cavitation, which is the formation of vapor bubbles that can interrupt smooth and continuous flow. This concept sets an upper limit on how high the top of the siphon can be relative to the exit point.

Bernoulli's Principle

Bernoulli's Principle states that in a streamline flow, the sum of the pressure energy, kinetic energy per unit volume, and gravitational potential energy per unit volume remains constant. This principle is used to relate the speed, elevation, and pressure at different points in the flow of an ideal, incompressible, and frictionless fluid, which is essential in analyzing the flow through a siphon.

Hydrostatic Pressure

Hydrostatic pressure refers to the pressure exerted by a fluid at rest due to the force of gravity. The pressure increases linearly with depth, and this concept is crucial for determining the pressure difference between two points in the tank and within the siphon, which in turn allows the calculation of the fluid velocity at the siphon’s outlet.

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