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Water flows at 2.5 m/s at a pressure of 3.2 × 10⁵ Pa in a pipe at ground level.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Water flows at $2.5\ \text{m/s}$ at a pressure of $3.2 \times 10^{5}\ \text{Pa}$ in a pipe at ground level. The pipe rises to $12\ \text{m}$ . Find the pressure up there (a) if the pipe keeps the same width, and (b) if it narrows so that the water moves at $5.0\ \text{m/s}$ . ( $g = 9.8\ \text{m/s}^2$ .)

Need a reminder? The key ideaShow

Bernoulli's equation: along a streamline of an ideal fluid in steady flow, $p + \tfrac12\rho v^2 + \rho gh$ is the same. In a level pipe, $p_1 - p_2 = \tfrac12\rho(v_2^2 - v_1^2)$ : faster means lower pressure.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← Water flows at 1.5 m/s in a level pipe 12 cm across, at a pressure of 2.0 × 10⁵ Pa.Show that Bernoulli's equation gives the pressure in a liquid at rest. →

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