A fluid is drawn up through a tube as shown in the figure.If the height difference from the top of the tank to the bottom of the siphon is H = 1.40 m,then what is the outflow speed? Assume the pressure is the same at the top of the tank and at the siphon outlet.

A)3.70 m/s
B)27.4 m/s
C)5.24 m/s
D)6.86 m/s

Question

A fluid is drawn up through a tube as shown in the figure.If the height difference from the top of the tank to the bottom of the siphon is H = 1.40 m,then what is the outflow speed? Assume the pressure is the same at the top of the tank and at the siphon outlet. 
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A)3.70 m/s 
B)27.4 m/s 
C)5.24 m/s 
D)6.86 m/s

Quizplus · Accepted Answer

The outflow speed can be determined using Bernoulli's equation:
P1 + (1/2)ρv1^2 + ρgh1 = P2 + (1/2)ρv2^2 + ρgh2
where P is the pressure, ρ is the density, v is the velocity, g is the acceleration due to gravity, and h is the height.

Assuming the pressure is the same at the top of the tank and at the siphon outlet (P1 = P2), and the velocity at the top of the tank is negligible (v1 = 0), we can simplify the equation to:
(1/2)ρv2^2 + ρgh2 = 0

Solving for v2, we get:
v2 = sqrt(2gh2) = sqrt(2gH) = 5.24 m/s

Therefore, the answer is C.

A Fluid Is Drawn Up Through a Tube as Shown