Question

the velocity of water flow, in feet per second, from a nozzle is given by ( v(p)=14.8sqrt{p} ), where ( p ) is the nozzle pressure, in pounds per square inch (psi). find the nozzle pressure if the water flow is 121 feet per second.
the nozzle pressure is approximately
(round the final answer to the nearest integer as needed. round all intermediate values to the nearest ten thousandth as needed.)

Explanation:

Step1: Substitute \(v(p) = 121\) into the formula

Given \(v(p)=14.8\sqrt{p}\), when \(v(p) = 121\), we have the equation \(121=14.8\sqrt{p}\).

Step2: Solve for \(\sqrt{p}\)

Divide both sides of the equation \(121 = 14.8\sqrt{p}\) by \(14.8\). So, \(\sqrt{p}=\frac{121}{14.8}\approx8.1757\).

Step3: Solve for \(p\)

Square both sides of the equation \(\sqrt{p}\approx8.1757\). Then \(p=(8.1757)^{2}\approx66.84\approx67\).

Answer:

\(67\)