2. THEORETICAL FOUNDATIONS
2.3 Calculation of operating point
2.3.1 Characteristic curve of the pump
To find the operating point of the pump, you must keep the number of revolutions (ω) constant. The height (H), power consumption (W) and performance (η) depends on the volumetric flow passing through the circuit.
The height can be calculated from Bernoulli's equation:
Where:
H = height (m).
g = gravity (m/s2).
P1= pressure at point 1 (bar).
P2= pressure at point 2 (bar).
u1= velocity at point 1 (m/s).
u2= velocity at point 2 (m/s).
z = height between the two manometers (m) (z = 0.25 m).
ρ = density of the fluid (in our case, ρ = 1000 kg/m3)
To carry out the calculation of the flow velocity (u), we must first determine the area of each tube, as they have a different diameter:
- In the case of calculating u1we need to calculate the area on the first stretch of the circuit:
- If we want to calculate the velocity of the fluid when it passes through the second stretch (u2), we need to calculate the area previously:
Where:
d1= 50 mm = 0.05 m
d2= 32 mm = 0.032 m
Thus, the value of velocity in two tranches (u1 and u2), is found with the formula of the volumetric flow in the energy balance:
This allows us to relate the height (y-axis) and volumetric flow (x-axis) using a graphic where you can see how the height decreases as the volumetric flow is greater. This is what we named the characteristic curve of the pump.