A piston-cylinder is producing a viscous oil flow, which has the flow rate of Q, radius R=1.5 mm, and stroke L-5 mm. The fluid density is p = 800 kg/m³ and the viscosity is μ = 0.5 Pa.s. The pressure to drive the flow is p=6.25 Pa. a. How many non-dimensional groupings can be obtained? Derive them. b. If the flow transitions at Re = V(2R)-2300. Is the generated flow laminar or turbulent given Q=20 mL/s? c. Assume the pressure gradient is uniform on the cross-section and can be calculated using. The velocity profile in the cylinder is u(r) = – [1 − (²]. Sketch the velocity profile. Calculate the shear stress at the R² Op cylinder wall and label the direction. d. Calculate the flow rate Q with the velocity profile in (c).. e. If the shear stress is uniform over the cross-section, i.e. T = C, what's the pressure gradient distribution and sketch it?

A hydraulic pump is shown in the following Figure, flow rate is 25 L/min, the diameter of suction pipe is 25mm, and the suction port of pump is higher than the oil surface of tank, the height is h, Kinematic viscosity of oil is 30×10“m²/s, density of oil is 900kg/m³. Only the pressure loss along the straight suction pipe with length h is 75 considered, if the vacuum degree at the inlet of pump is not bigger than 4500P ( 2 = R. a = 2, g=9.8) (1) Calculate the flow velocity in the suction pipe; (2) Judge the flow state in suction pipe; (3) Calculate the pressure loss along the straight suction pipe; (4) Calculate the oil absorption height h.