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Two lock gates of 7.5 m height are provi...

Two lock gates of `7.5 m` height are provided in a canal of `16 m` width meeting at an angle of `120^@`. Calculate the force acting on each gate when the depth of water in upstream side is `5 m`.

A

`1133kN`

B

`1200kN`

C

`578kN`

D

`1566kN`

Text Solution

Verified by Experts

The correct Answer is:
A
Height of lock gates `=7.5m`
Width of canal `=16m`
Inclination of gates `=120^@` and `H=5m`
From the geometry of the lock gates, we find that inclination of the lock gates with the walls
`a=(180^@-120^@)/2=30^@`
and width of each gate `=(16/2)/(cosalpha)=8/(cos30^@)=8/0.866=9.24m`
Therefore, wetted area of each gate
`A=5xx9.24=46.2m^(2)`
and force acting on each gate is
`F=gAxx(H/2)=9.81xx46.2xx(5/2)=1133kN`
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