Respuesta :
Answer:
(a) 408.16 m
(b) 10.87 m
Solution:
As per the question:
Height of the reservoir, h = 20 m
Pressure on the intake, [tex]P_{i} = 150\ kPa[/tex]
Pressure on the discharge, [tex]P_{d} = 450\ kPa[/tex]
Diameter of the pipes, d = 15 cm = 0.15 m
Now,
(a) The head supplied by the pump can be calculated as:
Applying Bernoulli's theorem:
[tex]\frac{P_{i}}{\rho g} + \frac{V_{i}^{2}}{2g} + z_{i} + H_{pump} = \frac{P_{d}}{\rho g} + \frac{V_{d}^{2}}{2g} + z_{d}[/tex]
where
[tex]V_{i} = V_{d}[/tex]
[tex]z_{i} = z_{d}[/tex]
Now, the above eqn becomes:
[tex]\frac{P_{i}}{\rho g} + H_{pump} = \frac{P_{d}}{\rho g}[/tex]
[tex]H_{pump} = \frac{P_{d} - {P_{i}}{\rho g}[/tex]
[tex]H_{pump} = \frac{450 - 150}{0.075\time 9.8} = 408.16\ m[/tex]
(b) To calculate the total Head loss between the pump and free discharge point:
[tex]\frac{P_{d}}{\rho g} + \frac{V_{d}^{2}}{2g} + z_{d} + H_{pump} = \frac{P'}{\rho g} + \frac{V'^{2}}{2g} + z' + H_{Loss}[/tex]
Since,
[tex]V_{d} = V'[/tex]
Thus
[tex]H_{Loss} = \frac{(450 - 0)\times 10^{3}}{9.8\times 1000} - 35 = 10.87 m[/tex]
