Respuesta :
The ratio of the cross-sectional area of the left side to the area of the right side is 24, using Bernoulli's theorem.
Given data ,
[tex]P_{left}[/tex] = 13,500 Pa
[tex]v_{left}[/tex] = 3.9m/s
[tex]P_{right}[/tex] = 17,700Pa
According to Bernoulli's theorem;
[tex]P_{left }[/tex] + [tex]\frac{1}{2}[/tex]ρ[tex](v_{left} )^{2}[/tex] = [tex]P_{right }[/tex] + [tex]\frac{1}{2}[/tex]ρ[tex](v_{right} )^{2}[/tex]
Putting in the values in the Bernoulli's theorem we get,
13,500 + [tex]\frac{1}{2} (3.9)^{2}[/tex] = 17,700 + [tex]\frac{1}{2}[/tex][tex](v_{right} )^{2}[/tex]
13,500 - 17,700 + [tex]\frac{1}{2} (3.9)^{2}[/tex] = [tex]\frac{1}{2}[/tex][tex](v_{right} )^{2}[/tex]
-4200 + [tex]\frac{1}{2} (3.9)^{2}[/tex] = [tex]\frac{1}{2}[/tex][tex](v_{right} )^{2}[/tex]
-4200 + 7.605 = [tex]\frac{1}{2}[/tex][tex](v_{right} )^{2}[/tex]
91.5m/s = [tex]v_{right}[/tex]
also, fluid flow in pipes is given as ,
[tex]a_{left} v_{left}= a_{right} v_{right}[/tex]
[tex]\frac{a_{left} }{a_{right} } = \frac{91.5}{3.9}[/tex]
[tex]\frac{aleft}{aright} = 24[/tex]
Therefore, the ratio of the cross-sectional area of the left side to the area of the right side is 24, using Bernoulli's theorem.
Learn more about Bernoulli's theorem here:
https://brainly.com/question/13098748
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