Answer
See answers.
Work Step by Step
Follow the hint and use Bernoulli’s equation with no flow, which means $v_1=v_2=0$. Let point 1 be the initial point, and point 2 be the final point.
$$P_1+\frac{1}{2}\rho v_1^2+\rho g y_1= P_2+\frac{1}{2}\rho v_2^2+\rho g y_2$$
$$P_1+\rho g y_1= P_2+\rho g y_2$$
$$P_2-P_1=\Delta P = \rho g (y_1- y_2)$$
A change in the y coordinate is the negative of the change in depth, h. Equation 10–3b refers to the depth.
$$\Delta P=-\rho g \Delta y=\rho g \Delta h $$
This was to be shown.
