Air flows through the tube shown in (Figure 1). Assume that air is an ideal fluid. Find the air speed v1 at point 1 and v2 at point 2 and the volume flow rate.

Derive the energy equation from Reynolds transport theorem

1. 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 = PV(2R) =2300. Is the generated flow laminar or turbulent given Q=20 mL/s? LL c. Assume the pressure gradient is uniform on the cross-section and can be calculated using OP=-. The velocity profile in the cylinder is u(r) = ax - [1-(²]. Sketch the velocity profile. Calculate the shear stress at the R² ap 2UÔI 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? L L. R

Transcribed Image Text:As part of a processing of biofuels, water is pumped into a circular tank with a diameter Dt. as shown in Figure Q3. The flowrate into the tank is Q₁ and the flowrate out is Q₂. When the vessel is heated, water evaporates. The average velocity at which the vapour rises across the entire tank is vevap- You may assume that water has a density of Pw, and vapour has a density of Pv. Acceleration due to gravity is g. 2₁ Vevap Q₂ => D₂ Figure Q3: Water being pumped through a heated evaporation tank. Find anexpressio  for the rate of chnage of the mass of water in the tank At time t= 0 the height of water in the tank is h0. Find an expression for the height as a function of time h(t) An alarm is triggered when the pressure at the bottom of the tank exceeds P alarm. Find an expression  for the time at which the alarm goes off