Respuesta :
Explanation:
Given that,
Diameter = 10 cm
Distance = 2 m
Speed [tex]v_{1}= 2\ m/s[/tex]
Speed [tex]v_{2}=7\ m/s[/tex]
Pressure in main pipe [tex]P_{1}=2\times10^{5}\ Pa[/tex]
(I). We need to calculate the diameter
Using equation of continuity
[tex]Av_{1}=Av_{2}[/tex]
[tex]\pi(\dfrac{d_{1}}{2})^2\times v_{1}=\pi(\dfrac{d_{2}}{2})^2\times v_{2}[/tex]
[tex](\dfrac{10}{2})^2\times2=(\dfrac{d_{2}}{2})^2\times7[/tex]
[tex]d_{2}=\sqrt{\dfrac{25\times2\times4}{7}}[/tex]
[tex]d_{2}=5.345\ cm[/tex]
(II). We need to calculate the pressure the gauge pressure
Using Bernoulli equation
[tex]P_{1}+\dfrac{1}{2}\rho v_{1}^2+\rho gh_{1}=P_{2}+\dfrac{1}{2}\rho v_{2}^2+\rho g h_{2}[/tex]
[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}=2\times10^{5}+\dfrac{1}{2}\times1000(4-49)-1000\times 9.8\times(5)[/tex]
[tex]P_{2}=1.28500\times10^{5}\ Pa[/tex]
(III). If it is possible to carry water to a faucet 17 m above ground,
Using Bernoulli equation
[tex]P_{1}+\dfrac{1}{2}\rho v_{1}^2+\rho gh=P_{3}+\dfrac{1}{2}\rho v_{3}^2+\rho g h_{3}[/tex]
[tex]P_{3}=P_{1}+\dfrac{1}{2}\rho v_{1}^2-\rho g(h_{1}-h_{3})[/tex]
Here, [tex]h_{3}=0[/tex]
Put the value in the equation
[tex]P_{3}=2\times10^{5}+\dfrac{1}{2}\times1000\times4-1000\times 9.8\times17[/tex]
[tex]P_{3}=3.5400\times10^{5}\ Pa[/tex]
Hence, This is required solution.
