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# Flow Around Immersed Bodies – Drag and Lift

الكلية كلية الهندسة     القسم  الهندسة البيئية     المرحلة 3
أستاذ المادة عدي عدنان جهاد الخيكاني       05/10/2012 11:49:32
Flow Around Immersed Bodies – Drag and Lift
When fluid flows around a body or the body moves in a fluid there is a relative motion between the fluid and the body. The body will experience a force in such a situation. In the case of a flat plate positioned parallel to the direction of the flow, the force is parallel to the surface.
But generally in the case of blunt bodies, the force will neither be parallel nor perpendicular to the surface. The force can be resolved into two components one parallel to the flow and the other perpendicular to the flow. The former may be called shear force and the other, the pressure force. The component parallel to the direction of motion is called drag force FD and the component perpendicular to the direction of motion is called lift force, FL. Determination of these forces is very important in many applications, an obvious example being aircraft wings. Simple analytical methods are found to be insufficient for the determination of such forces. So experimentally measured coefficients are used to compute drag and lift.

Drag Force and Coefficient of Drag
Drag is the component of force acting parallel to the direction of motion. Using the method of dimensional analysis the drag force can be related to flow Reynolds number by

FD/?A = f (Re) ……………….(10-31)
For generality velocity is indicated as V Defining coefficient of drag as the ratio of drag to dynamic pressure, it is seen that

CD = f (Re) …………….(10-32)
CD =FD/A (1/ 2) ?

This applies to viscous drag only. In case wave drag is encountered, then
CD = f (Re, Fr) ………..(10.3.3)
If compressibility effect is to be considered
CD = f (Re, M) …………. (10.3.4)
Friction coefficient over flat plate in laminar flow, at a location was defined by
Cfx = ?w /(1/2) ? A = 0.664/Rex
0.5. Over a given length the average value is obtained as twice this value. For a flat plate of length L, in laminar flow
CD = 1.328/ …………… (10.3.5)
In turbulent flow in the range 5 × 105 > Re < 107
CD = 0.074/ ………… (10.3.6)
For ReL up to 109, an empirical correlation due to Schlichting is
CD = 0.455 ……….. (10.3.7)
For combined laminar and turbulent flow in the range 5 × 105 > Re < 107
CD =(0 074/. )- (1740/ ) …………(10.3.8)
For the range 5 × 105 > Re < 109
CD =0 455/ - 1610./ …………..(10.3.9)
The values of CD for laminar flow is in the range 0.002 to 0.004.

Example 10.5. A ship having a wetted perimeter of 50 m and length of 140 m is to travel at 5 m/s. Determine the power required to overcome the skin friction. Assume kinematic
viscosity v = 1.4 × 10–6 m2/s. Density 1025 kg/m3
Re = 5 × 140/1.4 × 10–6 = 0.5 × 109,
So the equation applicable is 10.3.9
CD =0 455/ (log0.5 ×10^9 )^ 2. 58 - 1610/( 0.5× 10^9) = 1.719 × 10^–3
FD = CD A(1/2) ?u2 = (1.7179 × 10–3) (1/2) × 140 × 50 × 1025 × 52 N
= 0.154 × 106N
? Power = FD u = 0.154 × 10^6 × 5 = 0.77 × 106 W = 0.77 MW
Pressure Drag
When flow is perpendicular to blunt objects, like a plate or a disk, shear does not contribute to drag force. The drag is then mainly due to pressure difference between the faces. So it is called pressure drag. The drag coefficient is based on the frontal area (or projected area) of the object. In the case of airfoils the plan area is the basis for drag coefficient. The drag coefficient for same geometries are shown in Table 10.3.1 below. These are applicable for Re > 103.

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