Orifice Meter and Pitot Tube

The orifice meter is a device (cheaper than venturimeter) used for measuring the discharge of the liquid flowing through a pipe. It works on the same principle as that of venturimeter.

The pitot tube is a small open tube bent at right angle. It is used to measure the velocity of flow at the required point in a pipe. It is determined by measuring the rise of liquid in a tube.

Momentum Equation

The momentum equation is based on the law of momentum or momentum principle which states that "the net force acting on a mass of fluid is equal to the change in momentum of flow per unit time in that direction". Mathematically, force acting on the fluid,

F  = d(mv)/dt

where
mv = Momentum.

The impulse - momentum equation is given by

F x dt = d(mv)

It states that 'the impulse of a force (F) acting on a fluid mass (m) in a short interval of time (dt) is equal to the change of momentum [d(mv)] in the direction of force.

Orifice

What is an orifice and a mouthpiece? The orifice is a small opening in the wall or base of a vessel through which the fluid flows. A mouthpiece is an attachment in the form of a small tube or pipe fixed to the orifice. Its length is usually two to three times the diameter of orifice. It is used to increase the amount of discharge.

Hydraulic Coefficients

Hydraulic Coefficients include Coefficient of contraction, Coefficient of velocity, Coefficient of discharge and Coefficient of resistance. The following are the hydraulic coefficients:

1. Coefficient of contraction (Cc). It is defined as the ratio of area of jet at *vena contracta (ac) to the area of orifice (a).

The point at which the streamlines first become parallel is called vena contracta. The cross-sectional area of the jet at vena contrata is less than that of the orifice. The theoretical velocity of jet at vena contracta is given by


 
This expression is called Torricelli's theorem.

2. Coefficient of velocity (Cv). It is defined as the ratio of the actual velocity of the jet at vena contracta (v) to the theoretical velocity.

3. Coefficient of discharge (Cd). It is defined as the ratio of the actual discharge through the orifice (Q) to the theoretical discharge (Qth). The coefficient of discharge is equal to the product of Cc and Cv.

4. Coefficient of resistance (Cr). It is defined as the ratio of loss of head in the orifice to the head of water available at the exit of the orifice.

Note: The coefficient of velocity is determined experimentally by using the following relation, i.e.



where
x = Horizontal distance,
y = Vertical distance, and
H = Constant water head.

Important Expressions used in Orifices and Mouthpieces

The following are the important expressions used in orifices and mouthpieces including discharge through large rectangular orifice, discharge through wholly submerged orifice, and more:

(a) Discharge through a large rectangular orifice,



where
Cd = Coefficient of discharge,
b = Breadth of the orifice,
H1 = Height of the liquid above the top of the orifice, and
H2 = Height of the liquid above the bottom of the orifice.

(b) Discharge through a wholly submerged orifice,



where
H1 = Height of water (on the upstream side) above the top of the orifice,
H2 = Height of water (on the downstream side) above the bottom of the orifice, and
H = Difference between two water levels on either side of the orifice.

(c) Time required to empty the tank completely through an orifice at the bottom,



(d) Time required to empty the hemispherical tank through an orifice at the bottom,



where
R = Radius of hemispherical tank.

(e) Discharge through an external mouthpiece,



where
a = Cross-sectional area of the mouthpiece, and
H = Height of liquid above the mouthpiece.

(f) Discharge through the internal mouthpiece when it is running free,



(g) Discharge through the internal mouthpiece when it is running full,



Notes:

1. The re-entrant or Borda's mouthpiece is an internal mouthpiece.

2. If the jet of liquid after contraction does not touch, the sides of the mouthpieces, then the mouth piece,is said to be running free. In this case, the length of mouthpiece is equal to diameter of the orifice.

3. If the jet of liquid after contraction expands and fills up the whole mouthpiece, then the mouthpiece is said to be running full. In this case, the length of mouthpiece is more than three times the diameter of orifice.

Share with friends