Physics

Physics

Problem

Water flows steadily through a horizontal pipe that tapers from an internal diameter of 10 cm10\,\text{cm} at section 1 to 5.0 cm5.0\,\text{cm} at section 2. The pressure difference between the two sections is 1.8×104 Pa1.8\times10^{4}\,\text{Pa}, the pressure being higher at section 1. Calculate the volume flow rate of water in the pipe. (Take ρ=1000 kg m−3\rho = 1000\,\text{kg}\,\text{m}^{-3})
Intuitive explanation

This problem combines the continuity equation (mass is conserved, so flow rate is constant) with Bernoulli's principle (pressure and kinetic energy trade off as fluid speeds up). The key insight is that water accelerates as the pipe narrows, so the pressure must drop—and that pressure difference tells you how much faster it's moving. Use continuity to relate the two velocities, then Bernoulli to connect pressure drop to speed, and solve for the flow rate.

Intuitive explanation

This problem combines the continuity equation (mass is conserved, so flow rate is constant) with Bernoulli's principle (pressure and kinetic energy trade off as fluid speeds up). The key insight is that water accelerates as the pipe narrows, so the pressure must drop—and that pressure difference tells you how much faster it's moving. Use continuity to relate the two velocities, then Bernoulli to connect pressure drop to speed, and solve for the flow rate.

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