A garden hose is used to fill a large metal container which can hold 21.0 L of liquid. If the radius of the garden hose's nozzle is 1.1 cm, and the speed of the water at this point is 273.0 cm/s, how long (in seconds) would it take to fill the container with water, assuming that none of it splashes out?

Question

anonymous · Answer

We can model the rate of volume flow as$$\huge Q= \int\limits\int\limits_A v \cdot dA \implies Q=v_\text{avg}A$$Where:
Q = rate of flow
v = viscous flow (average velocity)
A = cross sectional area

The time it takes to fill a certain volume while observing the rate of volume flow is$$\huge t=\frac{V}{Q}$$Where:
t = time to fill the volume
V = volume
Q = rate of flow

anonymous · Answer

Sources: https://en.wikipedia.org/wiki/Volumetric_flow_rate http://faculty.wwu.edu/vawter/physicsnet/Topics/Pressure/VolumeFlowRate.html

michele_laino · Answer

correct!! @CShrix

anonymous · Answer

Yay :D