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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 3.70 105 Pa and a speed of 2.3 m/s. However, on the second floor, which is 3.6 m higher, the speed of the water is 3.6 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=3.30\times 10^5 Pa[/tex]

Explanation:

Given

For First Floor

[tex]P_1=3.7\times 10^5 Pa[/tex]

[tex]v_1=2.3 m/s[/tex]

[tex]z_1=0 m[/tex]

For second Floor

[tex]z_2=3.6 m[/tex]

[tex]v_2=3.6 m/s[/tex]

Applying Bernoulli's equation

[tex]P_1+\frac{1}{2}\rho v_1^2+\rho gz_1=P_2+\frac{1}{2}\rho v_2^2+\rho gz_2[/tex]

[tex]P_2=P_1+\frac{1}{2}(\rho v_1^2-\rho v_2^2)+\rho g(z_1-z_2)[/tex]

[tex]P_2=3.30\times 10^5 Pa[/tex]

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