Discharge through a rectangular orifice
Key FactsGyroscopic Couple: The rate of change of angular momentum () = (In the limit).
- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.
Blaise Pascal (1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.
Leonhard Euler (1707-1783) was a pioneering Swiss mathematician and physicist.
Discharge Through A Small Rectangular OrificeAn orifice is considered to be small, if the head of water above the orifice if over 5 times the height of the orifice. In a small rectangular orifice, the velocity of water in the entire cross-section of the jet is approximately constant, so the discharge can be approximately with the relation,
- = Coefficient of discharge for the orifice
- a = Cross sectional area of the orifice
- h = Height of the liquid above the center of the orifice
- b = Width of the orifice
- d = Depth of the orifice
Discharge Through A Large Rectangular OrificeWith a large rectangular orifice, the velocity of the liquid particles is not constant, because there is a considerable variation of effective pressure head over the height of an orifice: Velocity of liquid varies with the available pressure head of the liquid. Now consider a large rectangular orifice, in one side of of the tank, discharging water as shown in figure. Let,
- = Height of liquid above the top of the orifice
- = Height of liquid above the bottom of the orifice
- = Breadth of the orifice
- = Coefficient of discharge
Total discharge through the whole orifice may be found out by integrating the above equation between the limits and , i.e.
Example - Discharge through a large rectangular orifice
A large rectangular orifice of 1.5m wide and 0.5m deep is discharging water from a tank. If the water level in the tank is 3m above the top edge of the orifice, find the discharge through the orifice. Take coefficient of discharge for the orifice as 0.6.
- b = 1.5m
- d = 0.5m
- = 3m
- = 0.6
Discharge through the orifice, Q = 3.59 m3 /s