Question

A vertical plane metal gate size is 3 mx 3 m
holds water one side upto its top. The moment
of hydrostatic thrust on gate about its top edge,
in kN-m is ------------( Take g = 10 m/s^2) (1
marks )
Ans.
270
135
62.5
540​

Answer 1

Answer:

The hydrostatic thrust on gate at its top edge is 135KN-m

Explanation:

Given that,

The size of metal gate is 3m x 3m

Hydrostatic Force on the gate about top edge is given as

$F=ρg \frac{h}{2} A$

therefore,

$F=(1000kgm {}^{ - 3} )(10ms {}^{ - 2} )( \frac{3m}{2} )(3m \times 3m) = 135000N$

Note:We use half the height as centre of gravity is taken as point of reference

For the given situation,the pressure diagram will form a right angled triangle with sides 3m,3m

Hence,hydrostatic thrust is given as

$T _{h} = F \times \frac{h}{3} \\ \frac{h}{3} \: is \: distance \: from \: centre \: of \: gravity \: of \: triangle$

Therefore

$T _{h} = 135000N\times \frac{3m}{3} = 135KN - m$

#SPJ3