Measurement of discharge C.K. Pithawalla College of Engineering & Technology, Surat. C.K. Pithawalla College of Engineering & Technology, Surat. Measurement of discharge

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Measurement of discharge 1.Venturiemeter 2.Orificemeter 3.Nozzlemeter 4.Rotometer

Venturimeter

Construction A venturimeter is essentially a short pipe 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.

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.

Working 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.

Working Fig  Measurement of Flow by a Venturimeter

Working Therefore, Eq always overestimates the actual flow rate. In order to take this into account, a multiplying factor Cd, called the coefficient of discharge, is incorporated in the Eq as  The coefficient of discharge Cd is always less than unity and is defined as where, the theoretical discharge rate is predicted by the Eq with the measured value of ∆h, and the actual rate of discharge is the discharge rate measured in practice. Value of Cd for a venturimeter usually lies between 0.95 to 0.98.

2 orificemeter

Construction An orificemeter provides a simpler and cheaper arrangement for the measurement of fow through a pipe. An orificemeter is essentially a thin circular plate with a sharp edged concentric circular hole in it.

The orifice plate, being fixed at a section of the pipe, creates an obstruction to the flow by providing an opening in the form of an orifice to the flow passage. Fig   Flow through an Orificemeter The area A0 of the orifice is much smaller than the cross-sectional area of the pipe. The flow from an upstream section, where it is uniform, adjusts itself in such a way that it contracts until a section downstream the orifice plate is reached, where the vena contracta is formed, and then expands to fill the passage of the pipe. One of the pressure tapings is usually provided at a distance of one diameter upstream the orifice plate where the flow is almost uniform (Sec. 1-1) and the other at a distance of half a diameter downstream the orifice plate.

Working Fig   Flow through an Orificemeter

Considering the fluid to be ideal and the downstream pressure taping to be at the vena contracta (Sec. c-c), we can write, by applying Bernoulli’s theorem between Sec. 1-1 and Sec. c-c,

Corection in velocity a coefficient of contraction Cc is defined as, Cc = Ac /A0, where A0 is the area of the orifice, then Eq. can be written, with the help of Eq,  

The value of C depends upon the ratio of orifice to duct area, and the Reynolds number of flow. The main job in measuring the flow rate with the help of an orificemeter, is to find out accurately the value of C at the operating condition. The downstream manometer connection should strictly be made to the section where the vena contracta occurs, but this is not feasible as the vena contracta is somewhat variable in position and is difficult to realize.

In practice, various positions are used for the manometer connections and C is thereby affected. Determination of accurate values of C of an orificemeter at different operating conditions is known as calibration of the orifice meter.

Nozzle meter Fig A measurement Flow nozzle meter

Nozzle meter The flow nozzle as shown in Fig. is essentially a venturi meter with the divergent part omitted. Therefore the basic equations for calculation of flow rate are the same as those for a venturimeter. The dissipation of energy downstream of the throat due to flow separation is greater than that for a venturimeter. But this disadvantage is often offset by the lower cost of the nozzle. The downstream connection of the manometer may not necessarily be at the throat of the nozzle or at a point sufficiently far from the nozzle.

Nozzle meter The deviations are taken care of in the values of Cd, The coefficient Cd depends on the shape of the nozzle, the ratio of pipe to nozzle diameter and the Reynolds number of flow.

Roto meter

Pitot Tube for Flow Measurement

Construction The principle of flow measurement by Pitot tube was adopted first by a French Scientist Henri Pitot in 1732 for measuring velocities in the river. A right angled glass tube, large enough for capillary effects to be negligible, is used for the purpose. One end of the tube faces the flow while the other end is open to the atmosphere as shown in Fig.

Working: The liquid flows up the tube and when equilibrium is attained, the liquid reaches a height above the free surface of the water stream. The difference in level between the liquid in the glass tube and the free surface becomes the measure of dynamic pressure. Therefore, we can write, neglecting friction,

Working: where p0, p and V are the stagnation pressure, static pressure and velocity respectively at point A

Working: Fig - Simple Pitot Tube  (a) tube for measuring the Stagnation Pressure  (b) Static and Stagnation tubes together

For an open stream of liquid with a free surface, this single tube is suffcient to determine the velocity. But for a fluid flowing through a closed duct, the Pitot tube measures only the stagnation pressure and so the static pressure must be measured separately. Measurement of static pressure in this case is made at the boundary of the wall (Fig). The axis of the tube measuring the static pressure must be perpendicular to the boundary and free from burrs, so that the boundary is smooth and hence the streamlines adjacent to it are not curved. This is done to sense the static pressure only without any part of the dynamic pressure.

A Pitot tube is also inserted as shown (Fig) to sense the stagnation pressure. The ends of the Pitot tube, measuring the stagnation pressure, and the piezometric tube, measuring the static pressure, may be connected to a suitable differential manometer for the determination of flow velocity and hence the flow rate

Classification of orifice Orifices are classified based on the shape or the cross-sectional area as: Rectangular orifice Circular orifice Triangular orifice and Square orifice Orifices are classified based on the size of the orifice and the head of fluid above the orifice as: Small orifice and

Classification of orifice Large orifice Depending on the shape of the upstream edge of the orifices, they are classified as: Sharp-edged orifice and Bell-mouthed orifice They are also classified based on the nature of the discharge as: Partially submerged or drowned orifice Fully submerged or drowned orifice Free discharging orifices

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