A garden hose attached with a nozzle is used to fill a 20-gallon bucket. The inner diameter of the hose is 1 inch and it reduces to 0.5 inch at the nozzle exit. If the average velocity in the hose is 8ft/s, determine
a) the volume and mass flow rates of water through the hose.
b) how long it will take to fill the bucket with water.
c) the average velocity of water at the nozzle exit.

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

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