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An experiment is carried out using water with density 1000kgm-3 The experimental data plot of Q against (p1-p2 has a gradient of 7×10-4 If the pipe diameter is 25mm call the diameter of the orifice opening?
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An experiment is carried out using water with density 1000kgm-3 The ex...
Calculation of Orifice Opening Diameter
Given Data:
- Density of water (ρ) = 1000 kg/m³
- Gradient of Q against (p1-p2) = 7×10^-4
- Pipe diameter = 25 mm
Calculations:
- Convert the pipe diameter from mm to m: 25 mm = 0.025 m
- Calculate the area of the pipe using the formula A = πr², where r is the radius of the pipe (r = 0.0125 m)
- Area of the pipe (A) = π(0.0125)² = 4.91x10^-4 m²
- The gradient of the plot is given by the formula Q = CdA√2ρ(p1-p2), where Cd is the discharge coefficient
- Substituting the given values, we get: 7×10^-4 = Cd(4.91x10^-4)√(2x1000)(p1-p2)
- Solve for Cd: Cd = 0.356
- The discharge coefficient for an orifice is typically around 0.61
- Use the formula Cd = (Area of orifice opening/Area of pipe) to find the diameter of the orifice opening
- Substituting the values, we get: 0.61 = (πr²)/(4.91x10^-4)
- Solve for r: r = 0.043 m
- Convert the radius to diameter: Diameter of the orifice opening = 2r = 0.086 m = 86 mm
Conclusion:
The diameter of the orifice opening is calculated to be 86 mm.
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An experiment is carried out using water with density 1000kgm-3 The experimental data plot of Q against (p1-p2 has a gradient of 7×10-4 If the pipe diameter is 25mm call the diameter of the orifice opening?
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