Question

An incompressible fluid is flowing through a horizontal pipe with a constriction. The velocity of the fluid in the wide section of the pipe is 5.00 m/s and the velocity of the fluid in the narrow section of pipe is 8.00 m/s. The pressure of the fluid in the wide section is 200 kPa. What is the pressure in the narrow section of the pipe

Answer 1

The Bermoulli's  equation allows us to find the pressure in the narrow part of the pipe through which water circulates is:

             P = 500 Pa

Bernoulli's equation is the work-energy relationship for fluids that are liquids and gases.

           $P_1 + \frac{1}{2} \rho v_1^2 + \rho g y_1 = P2 + \frac{1}{2} \rho v_2^2 + \rho g y_2$

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

They indicate that the pipe is horizontal, that the pressure in the wide part P₁ = 200 kPa and the velocity is v₁ = 5 m / s and in the narrow part v₂=8.00 m/s, see attached.

Since the pipe is horizontal y₁ = y₂

           P₁ + ½ ρ v₁² = P₂ + ½ ρ v₂²

           P₂ = P₁ + ½ ρ (v₁² - v₂²)

Let's calculate

          P₂ = 200 10² + ½ ρ (5² - 8²)

          P₂ = 2 10⁴ - 19.5 ρ

For a specific calculation the value of the density of the fluid is needed, suppose that the fluid is water ρ = 1000 kg / m³

           P₂ = 2 10² - 19.5 1000

           P₂ = 500 Pa

In conclusion using the Bermoulli equation we can find the pressure in the narrow part of the pipe through which water circulates is:  

             P = 500 Pa

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