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Water is flowing at the rate of 40litres/sec through a tapering pipe. The diameters at the bottom and upper ends are 300m and 200mm respectively. If the intensities of pressure at the bottom and upper ends are 250kN/m² and 100kN/m² respectively, find the difference in datum head?
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Water is flowing at the rate of 40litres/sec through a tapering pipe. ...
Given data:
- Water flow rate = 40 litres/sec
- Diameter at the bottom end = 300 mm
- Diameter at the upper end = 200 mm
- Pressure intensity at the bottom end = 250 kN/m²
- Pressure intensity at the upper end = 100 kN/m²

Calculating the difference in datum head:

Step 1: Convert diameters to meters
- Diameter at the bottom end = 300 mm = 0.3 m
- Diameter at the upper end = 200 mm = 0.2 m

Step 2: Calculate the difference in cross-sectional areas
- Area at the bottom end = (π/4) x (0.3)^2 = 0.0707 m²
- Area at the upper end = (π/4) x (0.2)^2 = 0.0314 m²
- Difference in cross-sectional areas = 0.0707 - 0.0314 = 0.0393 m²

Step 3: Calculate the difference in pressure
- Pressure difference = Pressure at the bottom end - Pressure at the upper end
- Pressure difference = 250 kN/m² - 100 kN/m² = 150 kN/m²

Step 4: Calculate the difference in datum head
- Difference in datum head = (Pressure difference) / (Density x g x Difference in cross-sectional areas)
- Assuming the density of water as 1000 kg/m³ and acceleration due to gravity as 9.8 m/s²:
- Difference in datum head = (150 x 10^3 N/m²) / (1000 kg/m³ x 9.8 m/s² x 0.0393 m²)
- Difference in datum head = 0.389 m

Conclusion:
The difference in datum head between the bottom and upper ends of the tapering pipe is 0.389 meters.
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Water is flowing at the rate of 40litres/sec through a tapering pipe. The diameters at the bottom and upper ends are 300m and 200mm respectively. If the intensities of pressure at the bottom and upper ends are 250kN/m² and 100kN/m² respectively, find the difference in datum head?
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Water is flowing at the rate of 40litres/sec through a tapering pipe. The diameters at the bottom and upper ends are 300m and 200mm respectively. If the intensities of pressure at the bottom and upper ends are 250kN/m² and 100kN/m² respectively, find the difference in datum head? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Water is flowing at the rate of 40litres/sec through a tapering pipe. The diameters at the bottom and upper ends are 300m and 200mm respectively. If the intensities of pressure at the bottom and upper ends are 250kN/m² and 100kN/m² respectively, find the difference in datum head? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Water is flowing at the rate of 40litres/sec through a tapering pipe. The diameters at the bottom and upper ends are 300m and 200mm respectively. If the intensities of pressure at the bottom and upper ends are 250kN/m² and 100kN/m² respectively, find the difference in datum head?.
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