Question

A garden hose attached with a nozzle is used to fill a 10-gal bucket. The
inner diameter of the hose is 2 cm, and it reduces to 0.8 cm at the nozzle
exit.

Answer 1

If it takes 50 s to fill the bucket with water, we can determine the volume (m³/s) and mass flow rates (kg/s) of water through the hose. First, convert 10 gal to cubic metres:

$$V=10\cdot0.0038=0.038\text{ m}^3.$$

What is the rate at which the hose supplies the bucket with water?

$$Q=\frac{V}t=\frac{0.038}{50}=7.6\cdot10^{-4}\text{ m}^3/\text{s}.$$

The mass flow rate is (taking into consideration that 1 cubic metre weights 1000 kilograms):

$$Q=7.4\cdot10^{-4}\cdot1000=0.74\text{ kg/s}.$$