Water moves through a constricted pipe in steady, ideal flow. At the lower point shown in the figure below, the pressure is 1.70 x 10° Pa and the pipe radius is 2.50 cm. At the higher point located at y = 2.50 m, the pressure is 1.30 × 10° Pa and the pipe radius is 1.30 cm. P (a) Find the speed of flow in the lower section. 5.79 Your response differs from the correct answer by more than 100%. m/s (b) Find the speed of flow in the upper section. m/s (c) Find the volume flow rate through the pipe. m³/s

Solution. Please should correct

Water with a density of 1 g/cm³ flows through a horizontal pipe. The pipe cross-section tapers from 80 cm² to 40 cm² at a reducer. The static pressure before the reducer is 4 bar and the flow velocity is 4 m/s. The flow is incompressible and frictionless (inviscid). What static pressure is measured after the reducer?

3.3. Hagen-Poiseuille Flow: Fluid flows through a variable-diameter pipe as shown in the figure above. The pipe dimensions, flow rate, and fluid properties are as follows: L₁ L₂ L3 = 4 cm A₁ = 1 cm², A₂ = 4 cm². A3 = 0.25 cm² Q = 100 cm³/s p= 1.06 g/cm³ u = 3.5 cP segment 1 20₁ A₁ A₂ segment 2 L₂ Ap segment 3 L3 A3 → Use conservation of mass, the Hagen-Poiseuille relationship, and the electrical circuit analogy to answer the following: a) What should the total pressure drop be across the length of this variable-diameter pipe in order to provide the given flow rate Q? (Use the Hagen-Poiseuille relation and the electrical analogy; each segment is a resistor.) b) What is the average velocity u for each segment? (Mass conservation.) c) What is the Reynolds number (Re = – PHD) for each segment? d) What are the velocities at the centerline and at the wall for each segment?