Water pressure on Lock Gates
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.
OverviewWhenever a dam or a weir is constructed across a river or canal, the water levels on both the sides of the dam will be different. If it is desired to have navigation or boating in such a river or a canal, then a chamber, known as lock, is constructed between these two different water levels. Two sets of gates (one on the upstream side and the other on downstream side of the dam) are provided as shown in fig - 1. In order to transfer a boat from the upstream (i.e., from a higher water level to the downstream), the upstream gates are opened (while the downstream gates are closed) and water level in the chamber rises up to the upstream water level. The boat is then admitted in the chamber. Then upstream gates are closed and downstream gates are opened and the water level in the chamber is lowered to the downstream water level. Now the boat can proceed further downwards. If the boat is to be transferred from downstream to upstream side, the above procedure is reversed. Now consider a set of lock gates AB and BC hinged at the top and bottom at A and C respectively as shown in fig - 2(a). These gates will be held in contact at b by the water pressure, the water level being higher on the left hand side of the gates as shown in fig - 2(b). Let,
- P = Water pressure on the gate AB or BC acting at right angles on it
- F = Force exerted by the gate BC acting normally to the contact surface of the two gates AB and BC (also known as reaction between the two gates), and
- R = Reaction at the upper and lower hinge
- H1 = Height of water to the left side of the gate.
- A1 = Wetted area (of one of the gates) on left side of the gate
- P1 = Total pressure of the water on the left side of the gate
- H2, A2, P2 = Corresponding values for right side on the gate
- RT = Reaction of the top hinge, and
- RB = Reaction of bottom hinge
Similarly, Since the directions of P1 and P2 are in the opposite direction, therefore the resultant pressure,
We know that the pressure P1 will act through its center of pressure, which is at a height of from the bottom of the gate. Similarly, the pressure P2 will also act through its center of pressure which is also at a height of from the bottom of the gate. A little consideration will show, that half of the resultant pressure (i.e., P1 - P2 or P)will be resisted by the hinges of one lock gate (as the other half will be resisted by the other lock gates). 5) and (6) the values of RB and RT may be found out.
Example - Water pressure on lock gate
Two lock gates of 7.5m height are provided in a canal of 16m width meeting at an angle of . Calculate the force acting on each gate, when the depth of water on upstream side is 5m.
- Height of lock gates = 7.5m
- Width of lock gates = 16m
- Inclination of gates =
- H = 5m
and width of each gate = = = 9.24 m Wetted area of each gate, and force acting on each gate,
Force acting on each gate, P = 1133 KN