Aim of the Experiment
To determine the force exerted by a jet of water on stationary flat plate, hemispherical cup, and curved vane, and to verify theoretical force values using the momentum equation.
Theory
When a jet of fluid strikes a vane or plate, the fluid exerts a force on the surface due to the change in momentum. By Newton’s second law:
F = ρQ(V₂cosβ − V₁cosα)
For a stationary vane, applying the momentum equation in the direction of the jet:
Flat Plate (perpendicular to jet)
F = ρAV²
All momentum is transferred perpendicular to the plate. The fluid deflects at 90°, no component remains in the original jet direction.
Hemispherical Cup (concave face facing jet)
F = 2ρAV²
The jet reverses direction (180° deflection), delivering twice the force of a flat plate.
Curved Vane (deflection angle β)
F = ρAV²(1 + cosβ)
Where β is the angle of deflection. For β = 180° (hemispherical cup), F = 2ρAV².
Variables
ρ = density of water (1000 kg/m³)
A = cross-sectional area of the nozzle (m²)
V = jet velocity = Q/A (m/s)
Q = volumetric flow rate (m³/s)
Apparatus
- Impact of jet apparatus (FluidoSurge-X-124) with interchangeable vane targets
- Flat circular plate
- Hemispherical cup
- 45° and 90° curved vanes
- Nozzle with known diameter
- Hydraulic bench with flow measurement facility
- Weight balancing system (spring balance or deadweight platform)
- Stop-watch and measuring tank
Experimental Procedure
- Select the flat plate target and mount it on the apparatus. Note the nozzle diameter d.
- Switch on the hydraulic bench pump. Adjust the control valve to set the required flow rate.
- Measure the flow rate Q using the volumetric tank and stopwatch: Q = Volume / Time.
- Calculate the jet velocity: V = Q / A, where A = π d² / 4.
- Measure the force F exerted by the jet by reading the spring balance or adding weights to the balance platform until equilibrium is achieved.
- Calculate theoretical force using the relevant formula and compare with measured value.
- Repeat for 4–5 different flow rates.
- Replace the flat plate with the hemispherical cup and repeat steps 2–7.
- Replace with the curved vane and repeat.
Observation Table, Flat Plate
Nozzle diameter d = ___ mm | A = ___ m²
| S.No. | Volume (L) | Time (s) | Q (m³/s) | V = Q/A (m/s) | F Measured (N) | F Theoretical = ρAV² (N) | % Error |
|---|---|---|---|---|---|---|---|
| 1 | |||||||
| 2 | |||||||
| 3 | |||||||
| 4 |
Graph
Plot Measured Force F (Y-axis) vs ρAV² (X-axis) for each vane type. A straight line through the origin with slope = 1 for a flat plate, and slope = 2 for a hemispherical cup, confirms the theory.
Results and Conclusions
- The hemispherical cup produces approximately twice the force of a flat plate for the same jet velocity, consistent with the double momentum change.
- Experimental values are within ±10% of theoretical values, with differences attributable to friction losses and jet spreading.
- The results validate the momentum equation for jet-vane interaction, the principle underlying all impulse turbines.
Precautions
- Ensure the nozzle is aligned with the centre of the target vane.
- Take three measurements of flow rate for each setting and average them.
- Ensure the balancing platform is horizontal before taking readings.
- Do not exceed the maximum flow rate recommended for the apparatus.
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