Calculate the kinetic energy required to drive a fluid of density 4 x 10^-3 kg/m³ through a vertical pipe of height 100m maintained at a pressure of 0.02 N/m² and 0.08 N/m² at each end respectively. ​

Answers

Answer 1

Bernoulli's equation allows to find the result for the change of the kinetic energy of the fluid in the pipe is:  

Kinetic energy change is:  ΔK = 3.98 J

Fluid mechanics studies the movement of liquid and gases through pipes, for this it uses the Bernoulli's equation, which is the work and energy relationship for fluids.

       P₂ + ½ ρ v₂² + ρ g y₂ = P₁ + ½ ρ v₁² + ρ g y₁

Where the subscripts 1 and 2 are the two points of interest, P is the pressure, ρ the density, v the velocity and y the height.

The expression of kinetic energy in fluids is:

       K = ½ ρ v²

Let's substitute

       K₂ - K₁ = P₁-P₂ + ρ g (y₁-y₂)

      ΔK = P₁-P₂ + rho g (y₁-y₂)

Indicates the density of the fluid is 4 10⁻³ km / m³, there is a height difference of Δy = 100 m and the pressure of 0.08 Pa and 0.02 Pa.

      ΔK = (0.08 -0.02) + 4 10⁻³ 9.8 100

      ΔK = 0.06 + 3.92 ΔK = 3.98 J  

In conclusion using Bernoulli's equation we can find the result for the change in the kinetic energy of the fluid in the pipe is:

        ΔK = 3.98 J

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