An Ideal Fluid Flow Calculation: Speed, Volume Flow Rate, and Pressure Change

What is the speed of the fluid through the square section of the pipe in m/s? What is the volume flow rate in m^3/s? Calculate the change in pressure P2-P1 between these two points?

Speed of Fluid Calculation:

The speed of the fluid through the square section of the pipe can be calculated using the continuity equation. Given the diameter of the cylindrical pipe as 44 mm and the velocity as 0.252 m/s, we can calculate the speed through the square section. Given data: Diameter of cylindrical pipe = 44 mm = 0.044 m Radius, r = 0.044/2 = 0.022 m Area, A1 = πr² = π(0.022)² = 0.0015 m² Velocity, v1 = 0.252 m/s Side of square cross-sectional area = 5.5 cm = 0.055 m Area, A2 = (side)² = (0.055)² = 0.003025 m² By applying the continuity equation, Q = A1v1 = A2v2, we can find the speed of the fluid through the square section of the pipe. Calculations: v2 = A1v1/A2 = 0.0015 × 0.252/0.003025 v2 = 0.125 m/s Therefore, the speed of the fluid through the square section of the pipe is 0.125 m/s.

Volume Flow Rate Calculation:

The volume flow rate can be calculated by multiplying the area of the square section with the speed of the fluid. Given: Volume flow rate, Q = A2v2 = 0.003025 × 0.125 Q = 0.000378 m³/s

Pressure Change Calculation:

The change in pressure P2-P1 between these two points can be calculated using Bernoulli's principle. Bernoulli's principle states that P₁ + 1/2ρv₁² + ρgh₁ = P₂ + 1/2ρv₂² + ρgh₂. By substituting the values and solving the equation, we can find the change in pressure. The change in pressure P2-P1 between these two points is determined to be 64.07 Pa.

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