Venturimeter Discharge Analysis
Problem Statement
A Venturimeter of throat diameter 0.07 m is fitted in a 0.15 m diameter vertical pipe in which a liquid of relative density 0.8 flows downwards. Pressure gauges are fitted to the inlet and to the throat sections, with the throat located 0.9 m below the inlet. Taking the coefficient of the meter as 0.96, determine the discharge:
(a) When the pressure gauges read the same, and
(b) When the inlet gauge reads 15170 N/m2 higher than the throat gauge.
Given Data
| Pipe Diameter (d1) | 0.15 m |
| Pipe Area (A1) | π/4 × (0.15)2 = 0.01767 m2 |
| Throat Diameter (d2) | 0.07 m |
| Throat Area (A2) | π/4 × (0.07)2 = 0.00385 m2 |
| Vertical Distance (Z1 – Z2) | 0.9 m |
| Coefficient of Discharge (Cd) | 0.96 |
| Relative Density | 0.8 (i.e., ρ = 0.8 × 1000 = 800 kg/m3) |
| Acceleration due to Gravity (g) | 9.81 m/s2 |
1. Part (a): When P1 = P2
Head Difference Calculation:
h = (P1 – P2)/ρg + (Z1 – Z2) = 0 + 0.9 = 0.9 m
Discharge Calculation:
Substituting values:
Calculation yields:
2. Part (b): When P1 = P2 + 15170 N/m2
Head Difference Calculation:
h = (P1 – P2)/ρg + (Z1 – Z2) = 15170/(800×9.81) + 0.9 ≈ 2.83 m
Discharge Calculation:
Calculation yields:
Conclusion
For the given Venturimeter setup in a vertical pipe:
(a) When the pressure gauges read the same, the discharge is approximately 0.016 m3/s.
(b) When the inlet gauge reads 15170 N/m2 higher than the throat gauge, the discharge increases to approximately 0.0285 m3/s.
