Solve the problem.
-The velocity of water in $\mathrm{ft} / \mathrm{s}$ at the point of discharge is given by $\mathrm{v}=13.82 \sqrt{\mathrm{P}}$, where $\mathrm{P}$ is the pressure $\mathrm{lb} / \mathrm{in} .2$ of the water at the point of discharge. Find the rate of change of the velocity with respect to pressure if the pressure is $50.00 \mathrm{lb} / \mathrm{in}^{2}$.
A) $0.1382 \mathrm{ft} / \mathrm{s}$ per $\mathrm{lb} / \mathrm{in} .^{2}$
B) $1.95 \mathrm{ft} / \mathrm{s}$ per lb/in. ${ }^{2}$
C) $0.9772 \mathrm{ft} / \mathrm{s}$ per $\mathrm{lb} / \mathrm{in} .^{2}$
D) $48.86 \mathrm{ft} / \mathrm{s}$ per $\mathrm{lb} / \mathrm{in} .^{2}$

Question

Quizplus · Accepted Answer

The rate of change of velocity with respect to pressure is found by differentiating $v = 13.82 \sqrt{P}$ with respect to $P$, giving $\frac{dv}{dP} = \frac{13.82}{2\sqrt{P}}$. Substituting $P = 50$, we get $\frac{dv}{dP} = \frac{13.82}{2\sqrt{50}} = 0.9772 \mathrm{ft} / \mathrm{s}$ per $\mathrm{lb} / \mathrm{in} .^{2}$.

Solve the Problem ft/s\mathrm{ft} / \mathrm{s}ft/s At the Point of Discharge Is Given By

Solve the Problem $\mathrm{ft} / \mathrm{s}$ At the Point of Discharge Is Given By