Introduction: The Venturi meter is a device for measuring discharge in a pipe. It consists of a rapidly converging section which increases the velocity of flow and hence reduces the pressure. It then returns to the original dimensions of the pipe by a gently diverging 'diffuser' section. By measuring the pressure differences the discharge can be calculated. This is a particularly accurate method of flow measurement as energy loss is very small.
Applying Bernoulli along the streamline from point 1 to point 2 in the narrow throat of the Venturi meter we have
By the using the continuity equation we can eliminate the velocity u2,
Substituting this into and rearranging the Bernoulli equation we get
To get the theoretical discharge this is multiplied by the area. To get the actual discharge taking in to account the losses due to friction, we include a coefficient of discharge
This can also be expressed in terms of the manometer readings
Notice how this expression does not include any terms for the elevation or orientation (z1 or z2) of the Venturimeter. This means that the meter can be at any convenient angle to function.
The purpose of the diffuser in a Venturi meter is to assure gradual and steady deceleration after the throat. This is designed to ensure that the pressure rises again to something near to the original value before the Venturi meter. The angle of the diffuser is usually between 6 and 8 degrees. Wider than this and the flow might separate from the walls resulting in increased friction and energy and pressure loss. If the angle is less than this the meter becomes very long and pressure losses again become significant. The efficiency of the diffuser of increasing pressure back to the original is rarely greater than 80%.