A cylindrical tank of height $1,\text{m}$ and radius $0.5,\text{m}$ is full of water. A small pipe of radius $0.05,\text{m}$ is attached at the bottom of the tank, opening into a vertical tube that rises $0.5,\text{m}$ above the water surface. What is the gauge pressure at the opening of the pipe relative to atmospheric pressure?

Step-by-step solution

1. Pressure at a depth $h$ is given by $P=\rho gh$.
2. Here depth from water surface to pipe opening is the height of the tank: $h=1,\text{m}$.
3. Use $\rho =1000,{\text{kg/m}}^3$ and $g=9.8,{\text{m/s}}^2$.
4. Compute $P=1000\times 9.8\times 1=9800,\text{Pa}=9.8,\text{kPa}$.
5. Thus the gauge pressure at the opening is $9.8,\text{kPa}$ above atmospheric pressure.

Concept tested: Pressure at a depth depends only on depth, not pipe radius

Published 7 October 2026 · How this solution was prepared and checked