Venturimeter

Construction: A venturimeter is essentially a short pipe (Fig. 15.1) consisting of two conical parts with a short portion of uniform cross-section in between. This short portion has the minimum area and is known as the throat. The two conical portions have the same base diameter, but one is having a shorter length with a larger cone angle while the other is having a larger length with a smaller cone angle.

Fig 15.1  A Venturimeter

Working:

• The venturimeter is always used in a way that the upstream part of the flow takes place through the short conical portion while the downstream part of the flow through the long one.
  
  
• This ensures a rapid converging passage and a gradual diverging passage in the direction of flow to avoid the loss of energy due to separation. In course of a flow through the converging part, the velocity increases in the direction of flow according to the principle of continuity, while the pressure decreases according to Bernoulli’s theorem.
  
  
• The velocity reaches its maximum value and pressure reaches its minimum value at the throat. Subsequently, a decrease in the velocity and an increase in the pressure takes place in course of flow through the divergent part. This typical variation of fluid velocity and pressure by allowing it to flow through such a constricted convergent-divergent passage was first demonstrated by an Italian scientist Giovanni Battista Venturi in 1797.

Fig 15.2  Measurement of Flow by a Venturimeter

• Figure 15.2 shows that a venturimeter is inserted in an inclined pipe line in a vertical plane to measure the flow rate through the pipe. Let us consider a steady, ideal and one dimensional (along the axis of the venturi meter) flow of fluid. Under this situation, the velocity and pressure at any section will be uniform.
  
  
• Let the velocity and pressure at the inlet (Sec. 1) are V₁ and p₁ respectively, while those at the throat (Sec. 2) are V₂ and p₂. Now, applying Bernoulli’s equation between Secs 1 and 2, we get

	(15.1)
	(15.2)

where ρ is the density of fluid flowing through the venturimeter.

• From continuity,

(15.3)

where A₁ and A₂ are the cross-sectional areas of the venturi meter at its throat and inlet respectively.

• With the help of Eq. (15.3), Eq. (15.2) can be written as

	(15.4)

 where and are the piezometric pressure heads at sec. 1 and sec. 2 respectively, and are defined as

	(15.5a)
	(15.5b)

• Hence, the volume flow rate through the pipe is given by

(15.6)

(Venturimeter continued....),