Instant Notes: 5. Flow Meters
Venturi Meter

The basic equation for the venturi meter is obtained by writing the Bernoulli equation for incompressible fluids between the two sections 1 and 2. Friction is neglected, the meter is assumed to be horizontal.
Velocity at venturi throat (\(v_2\)) is given by \[v_2 = \frac{1}{\sqrt{1\beta^4}}\sqrt{\frac{2(P_1P_2)}{\rho}}\] where \(\beta=D_2/D_1\). The above equation applies strictly to the frictionless flow of noncompressible fluids. To account for the small friction loss between locations 1 and 2, the above equation is corrected by introducing an empirical factor \(C_v\), known as the venturi coefficient.

To make the pressure recovery large, the angle of downstream cone is small, so boundary layer separation is prevented and friction minimized. Since separation does not occur in a converging cross section, the upstream cone can be made shorter than the downstream cone with but little friction, and space and material are thereby conserved.

Experimental measurements show that for \(\text{Re} > 10000\) the frictional loss over the venturi meter is about 10 percent of \(\Delta P\). Where \(\Delta P\) is pressure drop measured by the manometer connected between the upstream and throat sections of venturi meter.

For \(\text{Re} > 10000\), \(C_v\) of venturi meter is constant at about 0.98. For smaller Reynolds numbers the coefficient decreases rapidly.