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中文Introduction
In fluid dynamics drag is the resistance force acting on a solid body moving in a fluid (liquid or gas). Drag is constituted off frictional forces acting in a direction parallel to the body plus the pressure forces acting perpendicularly on the surface of the body. For any solid object moving through any fluid, the drag is said to be the sum of all hydrodynamic forces acting in a direction of fluid flow. To understand the drag force a simple example can be considered. If someone holds his hand out of the window of a moving car, the drag (i.e. the wind force) will try to push the hand behind.
Determination of Boundary layer thickness
(refer page 640-656 of Mechanics of Fluids by Shames) Boundary layer thickness is defined as the distance above a surface where the flow velocity is 99% of free stream velocity.
The accomplishment of boundary layer height can be understood from the concept of displacement thickness.
Considering the above figure,
The practical interest in boundary layer lies between growth of boundary layer and skin friction on a surface, where, skin friction is dependent on surface drag. So, it would be convenient to have a relation of skin friction in terms of boundary layer thickness. The relationship can be derived from the momentum balance equation.
Considering the diagram below,
From Newtons law we know that,
ΣF = (momentum) out of control volume – (momentum) into control volume
Since the areas of interests are only in the X directions,
The above equation holds good for turbulent flow. For laminar flow This can be obtained by putting u/U as 2(y/δ)-(y/δ) 2 in equation 5 and integrating both sides. For laminar flow
Calculation for wind tunnel case
The following table shows the drag force on the plates at different length. Since Re is less than 5×105, laminar flow equations were used. Kinematic viscosity for air is considered to be 1.55×10-5 m2/sec and density of air is considered to be 1.248 kg/m3. Drag force for bottom plate is thrice the drag force of top plate.
Calculation for full scale
The following table shows the drag forces on full scale. Since the Re is more than 5×105, turbulent flow equations were used. The values for kinematic viscosity and density are same as before.
Conclusion
From the calculated results, it is evident that flow in case of wind tunnel case is laminar and so the boundary layer thickness is also more. The drag forces are small in magnitude due to the fact that, the velocity is less and so are the areas at different cross-sections. However, in full scale, the flow is turbulent and so; the boundary layer thickness also decreases.
In both the cases, the side plates experience the same drag forces at different cross-sections. The bottom plate experiences more drag forces due to roughness of the plate and it is considered to be thrice the values of the top plate in this particular case.
