Answer :
Answer:
a). [tex]$0.0436 \ ft^3/s$[/tex] , [tex]$2.72 \ lb \ m/s$[/tex]
b). [tex]$61.32 \ s$[/tex]
c). 32. ft/s
Explanation:
a). The volume flow rate of the water is given by :
[tex]$\dot V = uA$[/tex]
[tex]$=u \pi \left( \frac{d}{2}\right)^2$[/tex]
[tex]$=\frac{u \pi d^2}{4}$[/tex]
[tex]$=\frac{8\ ft/s \ \pi \left(\frac{1}{12}\right)^2}{4}$[/tex]
[tex]$= 0.0436 \ ft^3/s$[/tex]
The mass flow rate of the water is given by :
[tex]$\dot m = \rho \dot V$[/tex]
[tex]$= 62.4 \times 0.0436$[/tex]
[tex]$=2.72 \ lb \ m/s$[/tex]
b). The time taken to fill the container is
[tex]$\Delta t = \frac{V}{\dot V}$[/tex]
[tex]$=\frac{20 \ gal}{0.0436 \ ft^3/s}\left( \frac{1 \ ft^3}{7.4804 \ gal}\right)$[/tex]
[tex]$=61.32 \ s$[/tex]
c). The average velocity at the nozzle is :
[tex]$u=\frac{\dot V}{A}$[/tex]
[tex]$=\frac{\dot V}{\frac{\pi d^2}{4}}$[/tex]
[tex]$=\frac{0.0436}{\frac{\pi \left(\frac{0.5}{12}\right)^2}{4}}$[/tex]
= 32. ft/s