Sea water of density 1.03 $\times$ 10³ kg/m³ is in streamline flow through a Venturi meter.The cross-sectional areas of the main pipe and the constriction are 0.139 m² and 0.0464 m²,respectively,and the pressure difference between the two portions is 55.2 kPa.The velocity of flow in the main pipe is A)0.305 m/s B)1.73 m/s C)3.66 m/s D)11.0 m/s E)20.7 m/s

Question

Quizplus · Accepted Answer

We can use the Bernoulli's equation and continuity equation to solve the problem.

From the continuity equation,

A1V1 = A2V2

where A1 and V1 are the cross-sectional area and velocity of flow in the main pipe, and A2 and V2 are the cross-sectional area and velocity of flow in the constriction.

Rearranging the equation,

V1 = (A2/A1)V2

Now, using the Bernoulli's equation between the two portions,

P1 + (1/2)ρV1^2 = P2 + (1/2)ρV2^2

where P1 and P2 are the pressures at the two portions, and ρ is the density of sea water.

Rearranging the equation,

V1 = sqrt(2(P2 - P1)/ρ)

Substituting the given values,

V1 = sqrt(2(55.2 x 10^3)/(1.03 x 10^3)(0.139^2 - 0.0464^2))

V1 = 3.66 m/s

Therefore, the answer is choice C.

Sea Water of Density 1 ×\times× 103 Kg/m3 Is in Streamline Flow Through a Venturi Meter

Sea Water of Density 1 $\times$ 10³ Kg/m³ Is in Streamline Flow Through a Venturi Meter