Bernoulli's equation - The fountain

Problem statement:

A fountain shoots a vertical jet of water to a maximum height H = 25 m. The fountain has a d = 5 cm nozzle at ground level. The water pump is h = 3 m below the ground (see figure). If the pipe to the nozzle has a diameter D = 8 cm, what pressure must the pump of the fountain supply?

Givens: ρ = 103 kg/m3; p0 = 105 Pa; g = 10 m/s2

Bernoulli's equation - fountain

Ad blocker detected

Knowledge is free, but servers are not. Please consider supporting us by disabling your ad blocker on YouPhysics. Thanks!


Solution:

Let’s assume a steady flow. In this case we can use the continuity equation and Bernoulli’s equation to solve this problem.

In order to apply Bernoulli’s equation we must find the speed of water v2 when it exists the pump.

Ad blocker detected

Knowledge is free, but servers are not. Please consider supporting us by disabling your ad blocker on YouPhysics. Thanks!


Now, since we know the diameters of both pipes we can apply the continuity equation to states 1 and 2:

And isolating v2:

Both diameters are givens of this problem. We can also determine the water speed in state 1, v1, because we know the height H it reaches. At this point its speed will be zero Its acceleration is that of gravity, g, so:

Now we make use of Bernoulli’s equation between states 1 and 2. We take h = 0 at state 2. At the open end 1 of the pipe the pressure is atmospheric pressure p0.

Bernoulli’s equation is:

Isolating p2 and substituting:

Finally, substituting v1 as a function of H as well as the givens of the problem we obtain:

Make sure that you include units in your results.

The post Bernoulli's equation - The fountain appeared first on YouPhysics