Question

Water is circulating through a closed system of pipes in a two floor apartment. On the first floor, the water has a gauge pressure of 3.70 105 Pa and a speed of 2.4 m/s. However, on the second floor, which is 3.6 m higher, the speed of the water is 3.5 m/s. The speeds are different because the pipe diameters are different. What is the gauge pressure of the water on the second floor

Answer 1

The value of gauge pressure at outlet = -38557.224 pascal

Step-by-step explanation:

Apply Bernoulli' s Equation

`(P_(1))/(9810)` +
`(V_(1) ^(2))/(19.62)` +
`h_(1)` =
`(P_(2))/(9810)` +
`(V_(2) ^(2))/(19.62)` +
`h_(2)` --------------(1)

Where

`P_(1)` = Gauge pressure at inlet = 3.70105 pascal

`V_(1)` = velocity at inlet = 2.4
`(m)/(sec)`

`P_(2)` = Gauge pressure at outlet = we have to calculate

`V_(2)` = velocity at outlet = 3.5
`(m)/(sec)`

`h_(2) - h_(1)` = 3.6 m

Put all the values in equation (1) we get,

⇒
`(3.70105)/(9810)` +
`(2.4 ^(2))/(19.62)` =
`(P_(2))/(9810)` +
`(3.5 ^(2))/(19.62)` + 3.6

⇒ 0.294 =
`(P_(2))/(9810)` + 0.6244 + 3.6

⇒
`(P_(2))/(9810)` = 0.294 - 0.6244 - 3.6

⇒
`(P_(2))/(9810)` = - 3.9304

⇒
`P_(2)` = - 38557.224 pascal

This is the value of gauge pressure at outlet.