Answer :
Answer:
(a). The velocity head at elevation of 20 m is 6.52 m/s.
(b). The pressure head at elevation of 20 m is 26.42 m.
(c). The velocity is 6.52 m/s.
(d). The pressure head at elevation of 55 m is 16.42 m.
Explanation:
Given that,
Vertical diameter = 0.15 m
Rate =0.20 m³/s
Pressure = 210 kPa
Elevation = 25 m
We need to calculate the velocity
Using formula of velocity
[tex]Q=vA[/tex]
[tex]v=\dfrac{Q}{A}[/tex]
Put the value into the formula
[tex]v=\dfrac{0.20}{\pi\dfrac{D^2}{4}}[/tex]
[tex]v=\dfrac{0.20}{\pi\dfrac{0.15^2}{4}}[/tex]
[tex]v=11.31\ m/s[/tex]
Since, Q is constant, A is constant so v will be constant everywhere.
(a). We need to calculate the velocity head at elevation of 20 m
Using formula of velocity head
[tex]v'=\dfrac{v^2}{2g}[/tex]
Put the value into the formula
[tex]v'=\dfrac{11.31^2}{2\times9.8}[/tex]
[tex]v'=6.52\ m/s[/tex]
The velocity head at elevation of 20 m is 6.52 m/s.
(b). We need to calculate pressure head at elevation of 20 m,
Using Bernoulli equation
[tex]h+\dfrac{p}{\rho g}+\dfrac{v^2}{2g}=constant[/tex]
[tex]h+\dfrac{p}{\rho g}=constant[/tex]
Here, velocity is constant
At h = 20 m
[tex]20+P_{H}=25+\dfrac{210\times10^{3}}{1000\times9.8}[/tex]
[tex]P_{H=46.42-20[/tex]
[tex]P_{H}=26.42\ m[/tex]
The pressure head at elevation of 20 m is 26.42 m.
(c). We need to calculate the velocity head at elevation of 55 m,
The velocity is v'=6.52 m/s.
(d). We need to calculate the pressure head at elevation of 55 m
Using formula again
At h = 55 m
[tex]h=55+P_{H}[/tex]
[tex]55+P_{H}=25+46.42[/tex]
[tex]P_{H}=25-55+46.42\ m[/tex]
[tex]P_{H}=16.42\ m[/tex]
The pressure head at elevation of 55 m is 16.42 m.
Hence, this is the required solution.