Energy Analysis of a Suction Pipe
Problem Statement
A 100 mm diameter suction pipe leading to a pump carries a discharge of 0.03 m³/s of oil with a specific gravity of 0.85. The pressure at point A in the suction pipe is a vacuum of 180 mmHg. Determine the total energy head at point A with respect to a datum at the pump (Z = -1.2 m).
Given Data
| Diameter (d) | 100 mm = 0.1 m |
| Discharge (Q) | 0.03 m³/s |
| Specific Gravity of Oil (sp gr) | 0.85 |
| Vacuum at A | 180 mmHg (i.e. -0.18 m of Hg) |
| Density of Oil (ρ) | 0.85 × 1000 = 850 kg/m³ (approx.) |
| Acceleration due to Gravity (g) | 9.81 m/s² |
| Datum Head (Z) | -1.2 m |
| Density of Mercury (γHg) | 13.6 × 1000 = 13600 kg/m³ (approx.) |
1. Calculating Cross-sectional Area
A = (π/4) × d² = (π/4) × (0.1)² = 0.00785 m²
2. Calculating Velocity
Using the continuity equation, V = Q/A = 0.03 / 0.00785 ≈ 3.82 m/s
3. Converting Pressure to Pressure Head
The given vacuum is -180 mm Hg, or -0.18 m of Hg. The pressure at A is computed as:
P = γHg × g × (−0.18 m) = 13600 × 9.81 × (−0.18) ≈ −24015 Pa
4. Calculating Pressure Head (P/γ)
Here, γ (specific weight of oil) = 0.85 × 9.81 × 1000 ≈ 8339 N/m³.
Pressure head = P / γ = (−24015) / 8339 ≈ −2.88 m
5. Calculating Velocity Head
Velocity head = V²/(2g) = (3.82²)/(2 × 9.81) ≈ (14.59)/(19.62) ≈ 0.744 m
6. Determining Total Energy Head
According to Bernoulli’s equation (ignoring losses), the total energy head at point A is:
E = (P/γ) + (V²/(2g)) + Z
E = (−2.88) + 0.744 + (−1.2) ≈ −3.336 m
Physical Interpretation
The analysis shows that the suction pipe is operating at a negative total energy head of approximately −3.336 m. This indicates that, relative to the pump datum, the combined effects of the vacuum (negative pressure head), the kinetic energy, and the elevation contribute to a net energy deficit at point A. Such an analysis is crucial in pump selection and avoiding cavitation.
Conclusion
Based on the given data and application of Bernoulli’s equation, the total energy head at point A in the suction pipe is approximately −3.336 m. This result integrates the vacuum pressure, the velocity head, and the datum elevation, providing key insights for the pump’s suction performance.
