Water rises through a pipe. At a lower section, the pipe diameter is 4 cm and the water speed is 2 m/s. At a point 5 m vertically above it, the pipe diameter is 2 cm. Neglect viscosity and take ρ = 1000 kg/m³ and g = 10 m/s². What is the pressure difference P(lower) - P(upper)?
Options

Question

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

Options

G1 Physics · Accepted Answer

The upper diameter is half the lower diameter. Therefore the upper cross-sectional area is one-fourth of the lower area. From continuity, A(lower)v(lower) = A(upper)v(upper). Hence, v(upper) = 4v(lower) = 8 m/s. Apply Bernoulli's equation between the lower and upper sections: P(lower) + ½ρv(lower)² + ρgz(lower) = P(upper) + ½ρv(upper)² + ρgz(upper). Take z(upper)−z(lower) = 5 m. Therefore, P(lower)−P(upper) = ½ρ[v(upper)²−v(lower)²] + ρg[z(upper)−z(lower)]. Substitute: = ½×1000×(8²−2²) + 1000×1…

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