OBJECTIVES
To observe flow patterns under a sluice gate
To determine the relationship between upstream head and flow rate
To determine the discharge coefficient (Cd)
To analyze and discuss the results
APPARATUS REQUIRED
1. Flow channel with adjustable slope
2. Sluice gate with lifting mechanism
3. Two precision depth gauges
4. Restriction block for downstream control
5. Stopwatch (digital, 0.01s resolution)
6. Measuring tape (minimum 2m length)
7. Calibrated flow meter (optional)
THEORY
1. Sluice Gate Functionality
Sluice gates are hydraulic structures used to control water flow in open channels. The gate provides adjustable aperture for flow regulation, with complete closure capability when sealed.
Bernoulli’s Equation (Energy Conservation):
½ρv₁² + ρgh₁ = ½ρv₂² + ρgh₂
Where:
h = elevation height (m)
ρ = fluid density (kg/m³)
v = flow velocity (m/s)
g = gravitational acceleration (9.81 m/s²)
2. Flow Rate Calculation
The volumetric flow rate (Q) through the gate is given by:
Continuity Equation:
Q = A₂v₂ = bh₂v₂
Where:
A₂ = downstream flow area (m²)
b = width of sluice gate (m)
h₂ = downstream water depth (m)
3. Velocity and Discharge Relationships
Assuming uniform velocity profiles and h₁/h₂ > 5, the downstream velocity is:
Velocity Equation:
v₂ = √[2g(h₁ – h₂)]
The theoretical flow rate becomes:
Theoretical Discharge:
Qtheory = bh₂√[2g(h₁ – h₂)]
4. Discharge Coefficient
Actual flow incorporates a discharge coefficient (Cd) accounting for energy losses:
Actual Discharge:
Qactual = Cdbh₂√[2g(h₁ – h₂)]
Where Cd typically ranges 0.55-0.65 for free flow conditions (h₁/h₂ < 0.2). The coefficient depends on:
• Upstream/downstream depth ratio
• Gate opening height
• Flow contraction at the gate
• Boundary roughness
PROCEDURE
1. Channel Setup
• Level the flow channel and ensure smooth bed surface
• Measure and record channel width (b)
2. Gate Adjustment
• Position the sluice gate vertically at desired height (a)
• Ensure proper sealing when fully closed
3. Flow Establishment
• Gradually open inflow valve to establish steady flow
• Allow sufficient time for flow stabilization
4. Measurements
• Record upstream depth (h₁) 4-5 channel widths upstream
• Measure downstream depth (h₂) at vena contracta (~a/2 downstream)
• Observe and sketch flow patterns
5. Flow Rate Determination
• Measure volumetric flow rate using timed collection or flow meter
• Repeat for at least 3 different gate openings
CALCULATIONS
1. Theoretical Flow Rate
Qtheory = bh₂√[2g(h₁ – h₂)]
2. Actual Flow Rate
Qactual = Volume collected / Time (for volumetric method)
3. Discharge Coefficient
Cd = Qactual / Qtheory
4. Percentage Difference
% Difference = [(Qactual – Qtheory)/Qactual] × 100
SAMPLE RESULTS
| Trial |
h₁ (m) |
h₂ (m) |
Qactual (m³/s) |
Qtheory (m³/s) |
Cd |
% Difference |
| 1 |
0.25 |
0.08 |
0.0125 |
0.0201 |
0.622 |
60.8 |
| 2 |
0.30 |
0.10 |
0.0182 |
0.0298 |
0.611 |
63.7 |
| 3 |
0.35 |
0.12 |
0.0247 |
0.0403 |
0.613 |
63.2 |
DISCUSSION
1. Flow Patterns
• Observed free discharge with hydraulic jump at lower tailwater levels
• Submerged flow conditions occurred at higher downstream depths
2. Discharge Coefficient
• Average Cd = 0.615 ± 0.005 across trials
• Values consistent with literature (0.61 for free flow)
• Minor variations due to measurement uncertainties
3. Error Analysis
• Significant % difference (60-64%) highlights energy losses
• Main loss sources: contraction, friction, turbulence
• Depth measurement errors amplified in velocity calculation
CONCLUSIONS
1. Sluice gates effectively regulate flow with Cd ≈ 0.61 for free flow conditions
2. Energy losses account for ~60% difference between actual and theoretical flow
3. Discharge coefficient remains relatively constant for similar h₁/h₂ ratios
4. Proper depth measurement at vena contracta is critical for accurate results
PRECAUTIONS
1. Experimental Setup
• Ensure channel is perfectly level before measurements
• Verify gate vertical alignment and smooth operation
2. Measurements
• Allow sufficient time for flow stabilization before readings
• Measure depths perpendicular to flow to avoid waves
• Take multiple readings at each condition
3. Calculations
• Use consistent units throughout calculations
• Account for significant figures in final results
