Question

6. A garden hose attached to a nozzle is used to fill a 15-gal bucket. The inner diameter of the hose is 1.5 cm, and it reduces to 0.8 cm at the nozzle exit. If it takes 50 s to fill the bucket with water (density = 1 kg/L), determine (a) the volume and mass flow rates of water through the hose, and (b) the average velocity of water at the nozzle exit.

Answer 1

Answer: 1.135 L/s; 1.35 kg/s, 22.57 m/s

Step-by-step explanation:

Given

Volume of bucket
`V=15\ gal\approx 56.78\ L`

time to fill it
`t=50\ s`

Volume flow rate

`\dot{V}=(56.78)/(50)=1.135\ L/s\approx 1.135* 10^(-3)\ m^3/s`

The inner diameter of the hose
`D=1.5\ cm`

diameter of the nozzle exit
`d=0.8\ cm`

we can volume flow rate as

`\Rightarrow \dot{V}=Av\quad \quad \text{v=average velocity through nozzle exit}\\\\\Rightarrow 1.135* 10^(-3)=(\pi )/(4)d^2* v\\\\\Rightarrow 1.135* 10^(-3)=(\pi )/(4)(0.8* 10^(-2))^2* v\\\\\Rightarrow v=(4* 1.135* 10^(-3))/(\pi * 64* 10^(-6))=22.57\ m/s`

Mass flow rate

`\Rightarrow \dot{m}=\rho * \dot{V}\\\Rightarrow \dot{m}=1\ kg/L* 1.135\ L/s=1.35\ kg/s`