Solve the problem.
-The velocity of water $\mathrm { ft } / \mathrm { s }$ at the point of discharge is given by $\mathrm { v } = 12.80 \sqrt { \mathrm { P } }$, where $\mathrm { P }$ is the pressure lb/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 $20.00 \mathrm { lb } / \mathrm { in } ^ { 2 }$.
A) $2.86 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$
B) $28.62 \mathrm { ft } / \mathrm { s }$ per lb/in 2
C) $1.4311 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$
D) $0.3200 \mathrm { ft } / \mathrm { s }$ per $\mathrm { lb } / \mathrm { in } ^ { 2 }$

Question

Quizplus · Accepted Answer

To find the rate of change of velocity with respect to pressure, we differentiate the given equation with respect to $P$: $\frac{dv}{dP} = 12.80 \cdot \frac{1}{2} \cdot P^{-1/2} = 6.40 \cdot P^{-1/2}$. Substituting $P = 20.00 \, \mathrm{lb/in}^2$, we get $\frac{dv}{dP} = 6.40 \cdot (20.00)^{-1/2} = 1.4311 \, \mathrm{ft/s} \, \text{per} \, \mathrm{lb/in}^2$.

Solve the Problem ft/s\mathrm { ft } / \mathrm { s }ft/s

Solve the Problem $\mathrm { ft } / \mathrm { s }$