Question

A rectangular tank of $6m$ long, $2m$ broad, and $2m$ deep is full of water. find the thrust acting on the bottom of the tank. (Density of water, ${\rho }_w=1000kg/m^3$)

• A. $23.52\times {10}^{4}N$
• B. $23.52N$
• C. $11.76\times {10}^{4}N$
• D. $3.92\times {10}^{4}N$

Answer 1

The correct option is A $23.52\times {10}^{4}N$

Observe the figure above.

Since the tank is completely filled, $f=h=2\text{m}$

Given length $l=6\text{m}$ and width $w=2\text{m}$

Area of the base = $A=l\times w=6\times 2=12{\text{m}}^2$

We know that, pressure of a fluid at depth $d$ increases by $\rho gd$

If the pressure of fluid on the top layer is $P_0$ then pressure of the fluid at the base is $P_0+\rho gf$

Thrust exerted by the fluid on the base is $T=(P_0+\rho gf)A$

if $P_0=0$ we have

$T=\rho gfA=1000\times 9.8\times 2\times 12=235200\text{N}=23.52\times {10}^4\text{N}$