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

Answer:

The value of gauge pressure at outlet = -38557.224 pascal

Explanation:

Apply Bernoulli' s Equation

$\frac{P_{1}}{9810}$ + $\frac{V_{1} ^{2}}{19.62}$ + $h_{1}$ = $\frac{P_{2}}{9810}$ + $\frac{V_{2} ^{2}}{19.62}$ + $h_{2}$ --------------(1)

Where

$P_{1}$ =  Gauge pressure at inlet = 3.70105 pascal

$V_{1}$ = velocity at inlet =  2.4 $\frac{m}{sec}$

$P_{2}$ = Gauge pressure at outlet = we have to calculate

$V_{2}$ = velocity at outlet = 3.5 $\frac{m}{sec}$

$h_{2} - h_{1}$ = 3.6 m

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

⇒ $\frac{3.70105}{9810}$ + $\frac{2.4 ^{2}}{19.62}$ = $\frac{P_{2}}{9810}$ + $\frac{3.5 ^{2}}{19.62}$ + 3.6

⇒ 0.294 = $\frac{P_{2}}{9810}$ + 0.6244 + 3.6

⇒ $\frac{P_{2}}{9810}$ = 0.294 - 0.6244 - 3.6

⇒ $\frac{P_{2}}{9810}$ = - 3.9304

⇒ $P_{2}$ = - 38557.224 pascal

This is the value of gauge pressure at outlet.