A fountain with an opening of radius $0.015\,\text{m}$ shoots a stream of water vertically from ground level at $6.0\,\text{m/s}$. The density of water is $1000\,\text{kg/m}^3$.

Question

A fountain with an opening of radius $0.015\,\text{m}$ shoots a stream of water vertically from ground level at $6.0\,\text{m/s}$. The density of water is $1000\,\text{kg/m}^3$.(a) Calculate the volume rate of flow of water.
, (b) The fountain is fed by a pipe that at one point has a radius of $0.025\,\text{m}$ and is $2.5\,\text{m}$ below the fountain’s opening. Calculate the absolute pressure in the pipe at this point.
, (c) The fountain owner wants to launch the water $4.0\,\text{m}$ into the air with the same volume flow rate. A nozzle can be attached to change the size of the opening. Calculate the radius needed on this new nozzle.
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Jason · Accepted Answer

$\boxed{Q \approx 0.00424\,\text{m}^3/\text{s}}$
$\boxed{P_{\text{pipe}} \approx 1.42 \times 10^5\,\text{Pa}}$
$\boxed{r_{\text{new}} \approx 0.0123\,\text{m}}$

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