...Venturimeter... contd from previous slide

• If the pressure difference between Sections 1 and 2 is measured by a manometer as shown in Fig. 15.2, we can write

	(15.7)

where ρ_m is the density of the manometric liquid.

• Equation (15.7) shows that a manometer always registers a direct reading of the difference in piezometric pressures. Now, substitution of from Eq. (15.7) in Eq. (15.6) gives

(15.8)

• If the pipe along with the venturimeter is horizontal, then z₁ = z₂; and hence becomes h₁ − h₂, where h₁ and h₂ are the static pressure heads

• The manometric equation Eq. (15.7) then becomes

• Therefore, it is interesting to note that the final expression of flow rate, given by Eq. (15.8), in terms of manometer deflection ∆h, remains the same irrespective of whether the pipe-line along with the venturimeter connection is horizontal or not.
  
  
• Measured values of ∆h, the difference in piezometric pressures between Secs I and 2, for a real fluid will always be greater than that assumed in case of an ideal fluid because of frictional losses in addition to the change in momentum.
  
  
• Therefore, Eq. (15.8) always overestimates the actual flow rate. In order to take this into account, a multiplying factor C_d, called the coefficient of discharge, is incorporated in the Eq. (15.8) as

• The coefficient of discharge C_d is always less than unity and is defined as

where, the theoretical discharge rate is predicted by the Eq. (15.8) with the measured value of ∆h, and the actual rate of discharge is the discharge rate measured in practice. Value of C_d for a venturimeter usually lies between 0.95 to 0.98.