AM2530: Foundations of Fluid Mechanics Tutorial 3: Integral relations for control volume 1. The fluid in direct contact with a stationary solid boundary has zero velocity; there is no slip at the boundary. Thus the flow over a flat plate adheres to the plate surface and forms a boundary layer, as shown in Figure 1. The flow ahead of the plate is uniform with velocity V Ui; u 30 m / s . The velocity distribution within the boundary layer (0 ≤ y ≤ δ) along cd is approximated as u/U = 2(y/δ)-(y/δ) 2. The boundary-layer thickness at location d is δ = 5 mm. The fluid is air with density ρ = 1.24 kg/m3. Assuming the plate width perpendicular to the paper to be w=0.6 m, calculate the mass flow rate across surface bc of control volume abcd.
Figure 1 2. Water flows steadily through the 90º reducing elbow shown in Figure 2. At the inlet to the
elbow, the absolute pressure is 220 kPa and the cross-sectional area is 0.01 m2. At the outlet, the cross-sectional area is 0.0025 m2 and the velocity is 16 m/s. The elbow discharges to the atmosphere. Determine the force required to hold the elbow in place.
Figure 2
3. A horizontal water jet of constant velocity V impinges normally on a vertical flat plate and splashes off the sides in the vertical plane as shown in Figure3. The plate is moving toward the oncoming water jet with velocity 1 . If a force F is required to maintain the plate
2
V
stationary, how much force is required to move the plate toward the water jet?
Figure 3
4. A smoking lounge is to accommodate 15 heavy smokers (Figure 4). The minimum fresh air requirement for smoking lounges is specified to be 30 L/s per person (ASHRAE, Standard 62, 1989). Determine the minimum required flow rate of fresh air that needs to be supplied to the lounge and the diameter of the duct if the air velocity is not to exceed 8 m/s.
Figure 4
5. A fan is to be selected to ventilate a bathroom whose dimensions are 2m ˣ 3m ˣ 3m (Figure 5). The air velocity is not to exceed 8 m/s to minimize vibration and noise. The combined efficiency of the fan-motor unit to be used can be taken to be 50 percent. If the fan is to replace the entire volume of the air in 10 min, determine (a) the wattage of the fan-motor unit to be purchased, (b) the diameter of the fan casing, and (c) the pressure difference across the fan. Take the air density to be 1.25 kg/m3 and disregard the effect of the kinetic energy correction factors.
