Answer:
this anawer is much more longer than i expected
Step-by-step explanation:
a) To determine the flow rate when the pump is operated at 1450 rpm, the following formula can be used:
Q = (π/4) * D^2 * N * v / (60 * f * L), where
D = 70 mm = 0.07 m (diameter),
N = 1450 rpm (speed),
v = fluid velocity,
f = 0.02 (friction factor), and
L = 40 m (pipe length)
Substituting the given values, we get:
Q = (π/4) * 0.07^2 * 1450 * v / (60 * 0.02 * 40)
v = Q / [(π/4) * 0.07^2 * 1450 / (60 * 0.02 * 40)]
We can calculate the head loss due to friction, hf:
hf = f * (L/D) * (v^2 / (2 * g)), where
g = 9.8 m/s^2 (acceleration due to gravity)
Substituting the known values,
hf = 0.02 * (40/0.07) * (v^2 / (2 * 9.8))
v = √[(2 * 9.8 * hf) / (0.02 * (40/0.07))]
The head of water at the pump, h, can be calculated from the difference in water level between the two tanks:
h = 5 m (difference in water level)
The head loss due to the pump, hp, can be calculated using the following formula:
hp = h - hf
Substituting the known values,
hp = 5 - hf
hf = 5 - hp
v = √[(2 * 9.8 * (5 - hp)) / (0.02 * (40/0.07))]
Finally, the flow rate can be calculated:
Q = (π/4) * 0.07^2 * 1450 * v / (60 * 0.02 * 40)
b) (i) If a second identical pump is installed in series with pump B, the head available at the first pump, h1, is equal to the head developed by the second pump, h2. Thus,
h1 = h2
5 - hf1 = hf2
The head loss in each pipe is the same and can be calculated as follows:
hf = f * (L/D) * (v^2 / (2 * g))
Substituting the known values,
hf = 0.02 * (40/0.07) * (v^2 / (2 * 9.8))
The total head loss can be calculated as follows:
hf = hf1 + hf2
Substituting the known values,
hf = hf1 + hf1 = 2 * hf1
v = √[(2 * 9.8 * (5 - hf)) / (0.02 * (40/0.07))]
Q = (π/4) * 0.07^2 * 1450 * v / (60 * 0.02 * 40)
(ii) If a second identical pump is installed in parallel with pump B, the total flow rate will be equal to the sum of the flow rates through each pump. Thus,
Q = Q1 + Q2