Venturimeter Analysis for Flow Measurement
Problem Statement
A Venturimeter is to be fitted in a horizontal pipe of 0.15 m diameter to measure a flow of water which may be anything up to 240 m3/hour. The pressure head at the inlet for this flow is 18 m above atmospheric, and the pressure head at the throat must not be lower than 7 m below atmospheric. Between the inlet and the throat, there is an estimated frictional loss of 10% of the difference in pressure head between these points. Calculate the minimum allowable diameter for the throat.
Given Data
| Diameter of pipe (d1) | 0.15 m |
| Cross-sectional area (A1) | π/4 × (0.15)2 = 0.01767 m2 |
| Discharge (Q) | 240 m3/hour = 240/3600 = 0.0667 m3/s |
| Velocity at inlet (V1) | 3.77 m/s |
| Pressure head at inlet (P1/ρg) | 18 m |
| Pressure head at throat (P2/ρg) | -7 m |
| Frictional loss (hL) | 0.1 × (18 – (-7)) = 2.5 m |
| Acceleration due to Gravity (g) | 9.81 m/s2 |
1. Calculate Inlet Area and Velocity
The cross-sectional area of the pipe is:
The discharge in SI units is:
Therefore, the velocity at the inlet is:
2. Determine the Frictional Loss
With pressure heads:
The frictional head loss is:
3. Apply Bernoulli’s Equation
For a horizontal pipe (Z1 = Z2), Bernoulli’s equation between the inlet (section 1) and the throat (section 2) is:
Rearranging:
Substituting known values:
Simplifying:
Solving for V22:
4. Calculate the Minimum Throat Diameter
The cross-sectional area at the throat is:
Equating the area to the circular cross-section:
Solving for d2:
Thus, the minimum allowable throat diameter is approximately 63 mm.
Conclusion
For a maximum flow of 240 m3/hour with a pressure head of 18 m at the inlet and ensuring that the throat pressure head does not drop below -7 m (after accounting for a frictional loss of 2.5 m), the analysis shows that the minimum allowable throat diameter is approximately 63 mm.
