Conservation of Mass, Volume and Mass Flow Rate

Prequisite Knowledge
Conservation of Mass
Volume Flow Rate and Mass Flow Rate

Problem
A garden hose attached with a nozzle is used to fill a 25-gal container. The inner diameter of the hose is 0.75" and it reduces to 3/8" at the nozzle exit. The average velocity in the hose is 7 ft/s. Determine
1.) the volume flow rate of water through the hose
2.) the mass flow rates of the water through the hose
3.) how long it will take to fill the container with water
4.) the average velocity of water at the nozzle exit

Solution

1.) The volume flow rate of the water is:


V
= uA = u
πd 2
4
  =  
π(0.75/12)2
4
(7 ft/s)


V
= 0.0215 ft3/s

2.) The mass flow rate of the water is:


m
= ρ

V
= (62.4 lbm/ft3)*(0.0215 ft3/s)


m
= 1.34 lbm/s

3.) The time it takes to fill the container is:

Δ t =  
V

V
  =  
25 gal
0.0215 ft 3/s
(1 ft 3 / 7.4804 gal)

Δ t = 155.44 s

4.) The average discharge velocity of water at the nozzle exit is:

ue =  

V
Ae
  =  

V
πde2 / 4
  =  
0.0215 ft3/s
π(0.375/12 ft)2 / 4

ue = 28 ft/s