The problem is to calculate the force per unit width and the torque per unit width about the bottom of a lock gate which is produced when a fluid of depth $H$ and density $\rho$ lies at rest on one side of the gate, and fluid of depth $h<H$ and density $\rho$ lies at rest on the other side of the gate.
How great is this force if the depths of water are $1m$ and $3m$, and the gates are $3m$ wide. ( i know the answer to this is $120,00 N$).
I have manged to achieve an equation for the force $F=\frac{1}{2}\rho g(H_{1}^2-H_{2}^2)$ however when i substitute $H_{1}^2=9$ and $H_{2}^2=1$ i don't seem to get the force as $F=120,000$ N as required. so i'm stuck if anyone could help that would be great.