Discharge over a Stepped Notch
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.
OverviewA stepped notch is a combination of rectangular notches as shown in figure. It is thus obvious that the discharge over such a notch will be the sum of the discharges over the different rectangular notches. Consider a stepped notch as shown in figure. For the purpose of analysis, let us split up the notch into two rectangular notches 1 and 2. The total discharge over the notch will be the sum of the discharges over the two rectangular notches. Let,
- H1 = Height of the liquid above the sill of notch 1
- b1 = Breadth of notch 1
- H2, b2 = Corresponding values for notch 2, and
- Cd = Coefficient of discharge for both the notches
and the discharge over the notch 2,
Now the total discharge over the notch,
Example - Discharge over a Stepped Notch
Find the discharge in m3 /s over a stepped notch shown in figure. The level of water coincides with the top of the notch. Take Cd for all sections 0.6. All dimensions are in mm.
- Cd = 0.6
Discharge over the notch = 0.779 m3 /s