Question

Water is filled to a height H behind a dam of width w. The resultant force on dam is



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Answer 1

$\huge\underline\purple{\sf ♡ Answer:}$

$\large{\boxed{\sf F={\frac{1}{2}}\rho g×w{H}^{2}}}$

$\huge\underline\purple{\sf ♡ Solution:}$

Given :-

Height = H

Width of Dam = w

To find :-

Resultant force on dam (F) = ?

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We know that :-

$\large{\boxed{\sf Pressure (P)=\rho g H }}$

Here ,

$\large{♡}$$\large{\boxed{\sf Average\: Pressure (P_{avg}={\frac{P_{top}-P_{bottom}}{2}}}}$

$\large\implies{\sf {\frac{0+\rho gH}{2}}}$

$\large{\sf P_{avg}={\frac{\rho gH}{2}}}$

$\large{♡}$$\large{\boxed{\sf F=P_{avg}A }}$

Here ,

A = Area

which is equal to = Hw

On Putting value :-

$\large\implies{\sf {\frac{\rho gH}{2}}×Hw}$

$\large\implies{\sf {\frac{1}{2}}\rho gw{H}^{2}}$

$\huge\red{♡}$$\large\red{\boxed{\sf F={\frac{1}{2}}\rho g{H}^{2}}}$

Answer 2

yes it is correct mark brainlist