Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Continuity equation, kinematics and dynamics of flow
Question Statement:
A 200 m long horizontal pipe carries a discharge of 50 L s⁻¹. The centre line of the pipe is 5 m above the datum. The diameter of the pipe tapers from 200 mm to 100 mm. Using g = 9.81 m s⁻² and neglecting losses in the pipe, if the pressure at the larger end of the pipe is 100 kPa, the pressure at the other end of the pipe in kPa is __________.
Official Answer Key:
80.2 to 81.5
Step-by-Step Solution & Explanation
A₁ = (π/4)(0.2)² = 0.031416 m², A₂ = (π/4)(0.1)² = 0.0078540 m².
V₁ = Q/A₁ = 0.05/0.031416 = 1.5915 m/s; V₂ = Q/A₂ = 0.05/0.0078540 = 6.3662 m/s.
Since the pipe is horizontal (both centrelines at the same elevation, 5 m, cancels out), Bernoulli's equation reduces to:
P₁/ρg + V₁²/2g = P₂/ρg + V₂²/2g
P₁/ρg = 100,000/9810 = 10.1937 m; V₁²/2g = (1.5915)²/19.62 = 0.12911 m → LHS = 10.3228 m.
V₂²/2g = (6.3662)²/19.62 = 2.06565 m.
P₂/ρg = 10.3228 − 2.06565 = 8.2572 m → P₂ = 8.2572 × 9810 = 80,982 Pa ≈ 80.98 kPa.
Hydrology
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