1. Engine oil flows over a 5m long flat plate with a free stream velocity of 2m/s. Determine the drag force acting on top side of the plate per unit width. The density and kinematic viscosity of engine oil at 40oC are 876kg/m3 and 2.485 x 10-4 m2/s.Assumptions:a) The flow is steady and incompressible.b) The critical Reynolds number is Rec = 5 x 105.

2. Consider laminar flow of a fluid over a flat plate. Now the free stream velocity of the fluid is tripled. Determine the change in the drag force on the plate. Assume the flow to be laminar.

3. The local atmospheric pressure at an elevation of 1610m is 83.4 kPa. Air at this pressure and at 25oC flows with a velocity of 9m/s over a 2.5m x 5m flat plate. Determine the drag force acting on the top surface of the plate, If the air flows parallel to the (a) 5m long side and (b) 2.5m long side.

Properties of air at 25oC and 1 atm pressure from text book:Density = 1.184 kg/m3, D.V. = 1.849 x 10-5 kg/(ms), K.V. = 1.562 x 10-5 m2/s

4. The top surface of a passenger car of a train moving at a velocity of 95km/h is 2.1m side and 8m long. If the outdoor air at 1 atm and 25C, determine the drag force acting on the top surface of the car.

5. The drag coefficient of a car at the design conditions of 1 atm, 25oC and 90 km/h is to be determined experimentally in a large wind tunnel in a full scale test. The height and width of the car are 1.25m and 1.65m respectively. If the horizontal force acting on the car is measured to be 220 N, determine the total drag coefficient of this car. (Ans: 0.29)

6. A car is moving at a constant velocity of 110 km/h. Determine the upstream velocity to be used in fluid flow analysis if a) the air is calm, b) wind is blowing against the direction of motion of the car at 30km/h, and c) wind is blowing in the same direction of motion of the car at 30km/h. (Note: In fluid flow analysis, the velocity used is the relative velocity between the fluid and the solid body.)

7. Wind loading is a primary consideration in the design of the supporting mechanisms of billboards. Determine the wind force acting on a 3.7m high 6m wide billboard due to 90km/h winds in the normal direction when the atmospheric conditions are 98kPa and 5oC. (Ans:17,000N) check

8. A circular sign has a diameter of 50cm and is subjected to normal winds up to 150 km/h at 10C and 100kPa. Determine the drag force acting on the sign. Also determine the bending moment at the bottom of its pole whose height from the ground to the bottom of the sign is 1.5m. Disregard the drag on the pole.

9. A 1.2-m-external-diameter spherical tank is located outdoors at 1 atm and 25C and is subjected to winds at 48 km/h. Determine the drag force exerted on it by the wind. Answer: 16.7 N.

Fig.11.34

10. A 2.2 cm outer diameter pipe is to span across a river at a 30m wide section while being completely immersed in water. The average flow velocity of water is 4m/s and the water temperature is 15oC. Determine the drag force on the pipe by the river. The density and dynamic viscosity of water at 15oC are 999.1 kg/m3 and 1.138 x10-3 kg/ms. (Take the drag coefficient from the figure 11.34).

11. A 3cm OD pipe is to span across a river at a 30m wide section while being completely immersed in water. The average flow velocity of the water is 3m/s and its temperature is 20C. Determine the drag force exerted on the pipe by the river. (Ans: 4450N).

12. A long 5cm dia steam pipe passes through some area open to the wind. Determine the drag force acting on the pipe per unit of its length when the air is 1 atm and 10C and the wind is blowing across the pipe at a speed of 50km/h.

13. A 6mm diameter electrical transmission line is exposed to windy air. Determine the drag force exerted on a 160m long section of the wire during a windy day when the air is at 1atm and 15C and the wind is blowing across the transmission line at 65 km/h. The density and kinematic viscosity of air at 1 atm and 15C are = 1.225 kg/m3 and = 1.47010-5 m2/s.

14. A 6.1cm dia smooth ball rotating at 500 rpm is dropped in a water stream at 15C flowing at 1.2m/s. Determine the lift and drag force acting on the ball when it is first dropped in the water. The density and dynamic viscosity of water at 15C are = 999.1 kg/m3 and = 1.13810-3 kg/ms.

and

6.1 cmWater stream500 rpm1.2 m/sBall

15. During a high Reynolds number experiment the total drag force acting on a spherical body of diameter D = 12cm subjected to airflow at 1 atm and 5oC is measured to be 5.2N. The pressure drag acting on the body is calculated by integrating the pressure distribution measured by the use of pressure sensors throughout the surface to be 4.9N. Determine the friction drag coefficient of the sphere. (Ans: 0.0115)

AirVD = 12 cmHint: