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 3.7 × 105 Pa and a speed of 2.3 m/s. However, on the second floor, which is 3.7 m higher, the speed of the water is 3.9 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

`P_2= 3.3 * 10^5 Pa`

Step-by-step explanation:

given,

gauge pressure on the first floor (P₁)= 3.7 x 10⁵ Pa

speed of water (v₁)= 2.3 m/s

height of second floor = 3.7 m

speed of water (v₂)= 3.9 m/s

gauge pressure on the second floor = ?

taking datum at h₁

so, h₁= 0

Applying Bernoulli's equation

`P_2 = P_1 + (1)/(2)\rho (v_1^2-v_2^2)+ \rho g (h_1 - h_2)`

`P_2= 3.7 * 10^5 + (1)/(2)* 1000* (2.3^2-3.9^2)+ 1000* 9.8* (0-3.7)`

`P_2= 328780 Pa`

`P_2= 3.3 * 10^5 Pa`