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Engineering and Tech / Fluid Mechanics 2 / Chapter 5 / Problem 35P

Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala

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The water level of a tank on a building roof is 20 m above

Chapter 5, Problem 35P

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QUESTION:

Problem 35P

The water level of a tank on a building roof is 20 m above the ground. A hose leads from the tank bottom to the ground. The end of the hose has a nozzle, which is pointed straight up . What is the maximum height to which the water could rise? What factors would reduce this height?

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QUESTION:

Problem 35P

The water level of a tank on a building roof is 20 m above the ground. A hose leads from the tank bottom to the ground. The end of the hose has a nozzle, which is pointed straight up . What is the maximum height to which the water could rise? What factors would reduce this height?

ANSWER:

Solution 35P

We need to calculate the maximum height to which the water could rise through the nozzle. We have to apply Bernoulli’s equation to find the height.

Step 1

Bernoulli’s equation in this case,

$\frac{P{\ }_{1}}{\rho{}g}+\frac{v{{\ }_{1}}^{2}}{2g}+h{\ }_{1}=\frac{P{\ }_{2}}{\rho{}g}+\frac{{v{\ }_{2}}^{2}}{2g}+h{\ }_{2}$ …..(1)

Here, $P{\ }_{1}=$ pressure on water in the tank

$v{\ }_{1}=$ speed of water on the given height in the tank

$\rho{}=$ density of water

$h{\ }_{1}=$ height of water in the tank

$P{\ }_{2}=$ pressure on the water to has risen to the maximum height

$v{\ }_{2}=$ speed of water at the maximum height

$h{\ }_{2}=$ maximum height of water

$g=$ acceleration due to gravity

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