(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Water flows into a nozzle at 3.00 m/s at a pressure of 1.31*10^{5}Pa. What should the ratio of input to output diameter be if the flow is to remain steady? What is the flow speed at the exit?

2. Relevant equations

[tex]

P_{{\rm{input}}} + \frac{{\rho v_{{\rm{input}}}^2 }}{2} = P_{{\rm{atmosphere}}} + \frac{{\rho v_{{\rm{output}}}^{\rm{2}} }}{2}

[/tex]

[tex]A_1 v_1 = A_2 v_2 [/tex]

3. The attempt at a solution

My first guess is to simply say that a 1:1 inpututput ratio with the water flowing out at the same speed as it flows in should do the trick. But that would be too easy. I guess that I'm to assume that the pressure outside is air pressure. If so, am I doing it right?

[tex]

\begin{array}{l}

P_{{\rm{input}}} + \frac{{\rho v_{{\rm{input}}}^2 }}{2} = P_{{\rm{atmosphere}}} + \frac{{\rho v_{{\rm{output}}}^{\rm{2}} }}{2} \\

\\

P_{{\rm{input}}} + \frac{{\rho v_{{\rm{input}}}^2 }}{2} - P_{{\rm{atmosphere}}} = \frac{{\rho v_{{\rm{output}}}^{\rm{2}} }}{2} \\

\\

\frac{{2\left( {P_{{\rm{input}}} + \frac{{\rho v_{{\rm{input}}}^2 }}{2} - P_{{\rm{atmosphere}}} } \right)}}{\rho } = v_{{\rm{output}}}^{\rm{2}} \\

\\

v_{{\rm{output}}}^{} = \sqrt {\frac{{2\left( {P_{{\rm{input}}} + \frac{{\rho v_{{\rm{input}}}^2 }}{2} - P_{{\rm{atmosphere}}} } \right)}}{\rho }} \\

\\

v_{{\rm{output}}}^{} = \sqrt {\frac{{2\left( {1.31 \times 10^5 \,{\rm{Pa}} + \frac{{\left( {1000\frac{{{\rm{kg}}}}{{{\rm{m}}^{\rm{3}} }}} \right)\left( {3.00\,{\rm{m/s}}^{\rm{2}} } \right)}}{2} - 101.325 \times 10^3 \,{\rm{Pa}}} \right)}}{{\left( {1000\frac{{{\rm{kg}}}}{{{\rm{m}}^{\rm{3}} }}} \right)}}} = 5.58{\rm{ m/s}} \\

\end{array}

[/tex]

[tex]\begin{array}{l}

A_1 v_1 = A_2 v_2 \\

\\

\frac{{A_1 }}{{A_2 }} = \frac{{v_2 }}{{v_1 }} = \frac{{3.00\;{\rm{m/s}}}}{{{\rm{5}}{\rm{.58}}\,{\rm{m/s}}}} = 0.5376 \\

\end{array}[/tex]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Fluid problem

**Physics Forums | Science Articles, Homework Help, Discussion**