Question

find the force on a vertical triangular plate of height h and base as shown in figure due to fluid filled in it?

Answer 1

solution

diagram for this equation can be drawn like this

let us take the triangular plate ABC

let us assume a small element of length dx and width D

then force on this element can be given as

$dF=P dA$

P=pressure at element and dA is area of it

so

$dF=\rho gDxdx$

from triangle ABC and AEF we can write

$\frac{D}{w}=\frac{x}{h}\\$

$D=\frac{wx}{h}.....eq.2$

from eq.1 and eq.2

$dF=\rho gx^2\frac{w}{h}dx$

so by integrating we can find force on it

$\int dF=\int^h_0(\frac{\rho gw}{h}x^2dx)$

so

$F=\frac{\rho g wh^2}{3}$

above expression is for the force on triangular plate.