Water rises through a pipe. At a lower section, the diameter is 4 cm and the water speed is 2 m/s. At a point 5 m vertically above it, the diameter is 2 cm. Neglect viscosity and take ρ = 1000 kg/m³ and g = 10 m/s². If P(lower) − P(upper) = N kPa, find N.
Physics · Fluid Mechanics · equation of continuity and bornullie theorem
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Question

Water rises through a pipe. At a lower section, the diameter is 4 cm and the water speed is 2 m/s. At a point 5 m vertically above it, the diameter is 2 cm. Neglect viscosity and take ρ = 1000 kg/m³ and g = 10 m/s². If P(lower) − P(upper) = N kPa, find N.

Physics · Fluid Mechanics · equation of continuity and bornullie theorem

G1 Physics · Accepted Answer

The upper area is one-fourth of the lower area. Therefore, by continuity, v(upper) = 4v(lower) = 8 m/s. Using Bernoulli's equation, P(lower)−P(upper) = ½ρ[v(upper)²−v(lower)²] +ρg(5). Hence, = ½×1000×(64−4) +1000×10×5 = 30000+50000 = 80000 Pa = 80 kPa. Thus, N = 80.