Question

A rectangular tank is filled with water to a depth of 1.5 m. Its longest side measures 2.5 m. What is the moment of the force about the base on this side? Is it. a) 5.5 kN.m b) 9.2 kN.m c) 13.8 kN.m d) 27.6 kN.m e) 41.4 kN.m

Answer 1

Answer:

The correct answer is option 'c': 13.8 kNm

Explanation:

We know that moment of a force equals

$Moment=Force\times Arm$

The hydro static force is given by $Force=Pressure\times Area$

We know that the hydrostatic pressure on a rectangular surface in vertical position is given by $Pressure=\rho \times g\times h_{c.g}$

For the given rectangular surface we have $h_{c.g}=\frac{h}{2}=\frac{1.5}{2}=0.75m$

Thus applying the values we get force as

$Force=1000\times 9.81\times 0.75\times 1.5\times 2.5=27.59kN$

This pressure will act at center of pressure of the rectangular plate whose co-ordinates is given by h/3 from base

Thus applying the calculated values we get

$Moment=27.59\times \frac{1.5}{3}=13.8kN.m$