In the wide part of the horizontal pipe, water flows at a speed of V = 50 cm / s. Determine the speed

| January 19, 2021 | education

In the wide part of the horizontal pipe, water flows at a speed of V = 50 cm / s. Determine the speed of water flow in the narrow part of the pipe, if the pressure difference in the wide part and in the narrow part is ΔР = 1.33 kPa

Given: V1 (water velocity in the wide part of the pipe) = 50 cm / s = 0.5 m / s; ΔP (pressure difference) = 1.33 kPa = 1.33 * 10 ^ 3 Pa; ρw (water density) = 1000 kg / m3.

The flow rate in the narrow part of the pipe is determined using Bernoulli’s law: ρw * V12 / 2 + P1 + ρw * g * h1 = ρw * V2 ^ 2/2 + P2 + ρw * g * h2.

For a horizontal pipe: ρw * g * h1 = ρw * g * h2 and ρw * V1 ^ 2/2 + P1 = ρw * V2 ^ 2/2 + P2, whence V2 = √ (2 * (ρw * V12 / 2 + ΔР) / ρв).

Calculation: V2 = √ (2 * (1000 * 0.5 ^ 2/2 + 1.33 * 10 ^ 3) / 1000) = 1.7 m / s.



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