Respuesta :
Answer:
The speed of the water jet emerging from the nozzle is 24.21 m/s.
Explanation:
Given that,
Height = 9.1 m
Diameter =1.8 inch
Gauge pressure = 348.875 kPa
We need to calculate the speed of the water jet emerging from the nozzle
Using Bernoulli's equation
[tex]\dfrac{1}{2}\rho(v_{n}^2-v_{p}^2)=P_{gauge}-\rho gh[/tex]
[tex](v_{n}^2-v_{p}^2)=(\dfrac{2}{\rho})P_{gauge}-2gh[/tex]
[tex]v_{n}^2-(\dfrac{A_{n}}{A_{p}})^2v_{n}^2=(\dfrac{2}{\rho})P_{gauge}-2gh[/tex]
[tex]v_{n}^2-(\dfrac{r_{n}}{r_{p}})^4v_{n}^2=(\dfrac{2}{\rho})P_{gauge}-2gh[/tex]
[tex]v_{n}^2=\dfrac{(\dfrac{2}{\rho})P_{gauge}-2gh}{1-(\dfrac{r_{n}}{r_{p}})^4}[/tex]
[tex]v_{n}=\sqrt{\dfrac{(\dfrac{2}{\rho})P_{gauge}-2gh}{1-(\dfrac{r_{n}}{r_{p}})^4}}[/tex]
Put the value into the formula
[tex]v_{n}=\sqrt{\dfrac{\dfrac{2}{1000}\times348.875\times10^{3}-2\times9.8\times9.1}{1-\dfrac{(0.9)^4}{(1.55)^4}}}[/tex]
[tex]v_{n}=24.21\ m/s[/tex]
Hence, The speed of the water jet emerging from the nozzle is 24.21 m/s.
