Problems

01

Fluid force on a triangular plate

Find the total force on the submerged vertical plate that is an isosceles triangle with (bottom) base $1\mathrm{m}$ and height $2\mathrm{m}$, and assume it is submerged with the upper vertex $3\mathrm{m}$ below the surface. Liquid is oil with density $\rho =900\mathrm{k}\mathrm{g}/{\mathrm{m}}^3$.

02

Fluid force on a parabolic plate

A parabolic plate is submerged vertically in water as in the figure:

The shape of the plate is bounded below by $y=x^2$ and above by the line $y=1$. (Note that $y$ increases going up in this coordinate system.)

Compute the total fluid force on this plate.

(Hint: your integrand should contain $(1-y)$ as a factor.)

03

Fluid force on triangular plates

For diagrams 1, 2, 3 (L to R) below, set up an integral to compute the hydrostatic force on the plate.

04

Fluid force on trapezoidal plates

For diagrams 1, 2, 3 (L to R) below, set up an integral to compute the hydrostatic force on the plate.

05

Fluid force on circular plates

For diagrams 1, 2, 3 (L to R) below, set up an integral to compute the hydrostatic force on the plate.