Answer to Question #190774 in Civil and Environmental Engineering for John Prats

Question

Determine the hydrostatic force on a triangular plate that is submerged in water.

6m wide and 4m high.

Answer 1

hydrostatic force = pressure $\times Area$

pressure = $\rho gdy$

= $1000 \times 9.8 \times dy$

from similar triangles

$\frac{6}{w}= \frac{4}{y}$

$w= \frac{3}{2}y$

force therefore = $1000\times 9.8\times (4-y)(\frac{3}{2})dy$

= $\int_0^4 9800\times (4-y)(\frac{3}{2})dy$

hydrostatic force = $156800 N$