a) Speed on the second floor is equal to 3.90 m/s
b) Water pressure on the second floor is 240000 Pa.
In fluid dynamics, Bernoulli's principle can be described as an increase in the speed of fluid occurring simultaneously with a decrease in static pressure or the fluid's potential energy.
The constant can be normalized in the Bernoulli equation. A common approach is total head or energy head H:
[tex]{\displaystyle H=z+{\frac {p}{\rho g}}+{\frac {v^{2}}{2g}}=h+{\frac {v^{2}}{2g}},}[/tex]
a) speed on the second floor can be calculated as:
[tex]Q_1=Q_2[/tex]
[tex]A_1V_1=A_2V_2[/tex]
[tex]\displaystyle \frac{\pi }{4}(d_1^2) \times V_1 = \frac{\pi }{4}(d_2^2) \times V_2[/tex]
[tex](2.5)^2\times 0.90 =(1.2)^2\times V_2[/tex]
V₂= 3.90 m/s
b) water pressure on the second floor can be calculated as:
[tex]{\displaystyle {\frac {P_1}{\rho g}}+{\frac {V_1^{2}}{2g}}+h_1 = {\frac {P_2}{\rho g} +{\frac {V_2^{2}}{2g}}} +h_2[/tex]
[tex]{\displaystyle {\frac {170\times 1000}{9.80\times 1000}}+{\frac {(0.90)^{2}}{2\times 9.80}}+7.6 = {\frac {P_2}{\rho g} +{\frac {(3.90)^{2}}{2\times 9.80}}}[/tex] here [tex]h_1-h_2 = 7.6[/tex]
[tex]{\displaystyle {\frac {P_2}{\rho g} = 24.215[/tex]
P₂ = 240000 Pa
Learn more about Bernoulli's principle, here:
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