Siphon - Explanation Using Bernoulli's Equation

Explanation Using Bernoulli's Equation

Bernoulli's equation may be applied to a siphon to derive the flow rate and maximum height of the siphon.

Let the surface of the upper reservoir be the reference elevation.

Let point A be the start point of siphon, immersed within the higher reservoir and at a depth −d below the surface of the upper reservoir.

Let point B be the intermediate high point on the siphon tube at height +h_B above the surface of the upper reservoir.

Let point C be the drain point of the siphon at height −h_C below the surface of the upper reservoir.

Bernoulli's equation:

= fluid velocity along the streamline

= gravitational acceleration downwards

= elevation in gravity field

= pressure along the streamline

= fluid density

Apply Bernoulli's equation to the surface of the upper reservoir. The surface is technically falling as the upper reservoir is being drained. However, for this example we will assume the reservoir to be infinite and the velocity of the surface may be set to zero. Furthermore, the pressure at both the surface and the exit point C is atmospheric pressure. Thus:

(Equation 1.)

Apply Bernoulli's equation to point A at the start of the siphon tube in the upper reservoir where P = P_A, v = v_A and y = −d

(Equation 2.)

Apply Bernoulli's equation to point B at the intermediate high point of the siphon tube where P = P_B, v = v_B and y = h_B

(Equation 3.)

Apply Bernoulli's equation to point C where the siphon empties. Where v = v_C and y = −h_C. Furthermore, the pressure at the exit point is atmospheric pressure. Thus:

(Equation 4.)