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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?

Respuesta :

Answer:

 [tex]P_2= 3.3 \times 10^5 Pa[/tex]

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

 [tex]P_2 = P_1 + \dfrac{1}{2}\rho (v_1^2-v_2^2)+ \rho g (h_1 - h_2)[/tex]

 [tex]P_2= 3.7 \times 10^5 + \dfrac{1}{2}\times 1000\times (2.3^2-3.9^2)+ 1000\times 9.8\times (0-3.7)[/tex]

 [tex]P_2= 328780 Pa[/tex]

 [tex]P_2= 3.3 \times 10^5 Pa[/tex]