Dam Hydrostatics

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Physics
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Hydrostatics question on dam

Find hydrostatic thrust Pasted image 20241031135702

Forces on the wall are imposed by the vertical pressure of the water above.

This creates a Pressure Gradient down the wall. This will be linear, due to the compounding weight of water above each new bit of depth.

Pasted image 20241031145915

From pressure equations, the pressure is the force per unit area, so: $F = PA$ P in this case is caused purely by the water’s weight. In fact we can do this as $\bar{P}$. This is the average pressure on the surface. Hydrostatic pressure is give by:

\[\bar{P} = \rho g \bar{h}\]

Where $\rho$ is the water’s density, $g$ is the acceleration due to gravity and $\bar{h}$ is the average depth.

\[F = (\rho g (h_0 + h_x) / 2) A\]

It is also possible to do this with an integral:

\[F = PA\] \[dF = PdA\] \[F_y = \int P dA\] \[dA = wdy\] \[F = w \int^y_0 \rho gydy\] \[F = w \rho g[\frac{y^2}{2} - 0]\]

This is essentially the same, but more interesting and demonstrates integral

Dam Hydrostatics

Tutoring

Hydrostatics question on dam