HF 111 PARTICLE DRAG COEFFICIENTS

1. GENERAL DESCRIPTIONThe apparatus is designed to study the drag of particle in a liquid under various Reynold numbers.This is done by dropping a particle into a vertical liquid column and timing its fall between two points. Particle cross section is no more than 1% of the tube cross section. Various sizes and density of particles are supplied including stream lined shaped objects.A guide at the top of the tube is provided to minimize disturbance to the liquid. Double valves at the bottom of the tubes provide a mean for particle removal with minimum loss of the liquid. A fluorescent tube light at the back of the liquid tube allows clear observation of the particle fall.1.1 technical Data1.1.1 Glass tube: Two 100mm outside diameter x1,5m long1.1.2 Tube top with guide: 2 ea1.1.3 Tube bottom with valves: 2 ea1.1.4 Ball spheres:1.1.4.1 Steel: Diameter: 3, 6, 9 mm1.1.4.2 Glass or plastics: 2 sizes diameter1.1.5 Streamlined object: Steel, diameter 6 and 9 mm1.1.6 Fluorescent lamp: 40 W1.1.7 Stop watch: 1 ea1.1.8 Power supply: 220V, 1 Ph, 50 Hz. Other power supply is available on1.2 Typical Test1.2.1 Measurement of drag coefficients of sphere under various Reynold Numbers1.2.2 Effect of [article shape on rate of fall and drag coefficient1.2.3 Effect of boundary layer separation on motion of sphere1.2.4 Exploration of dynamic similarity

2. THEORYWhen a body is completely immersed in a relatively large expanse of fluid,the fluid exerts a resultant force on the body arising from the relative motion between the body and the fluid. In common practice, this resultant force is resolved into two kinds or components of forces as shown in figure 2. The first force component is parallel to the motion of the body and againsts the movement direction of the body. This component of force is thereforce called Drag Force.On the other hand, the second force component which acts at right angle to the motion of the body is called Lift Force. This lift force enables the airplane to float in the air.

2.1DragDrag force on a body may be determined by the following equation:

Where,Fd= Drag force, NCd= Drag coefficient, Dimensionless= Density of fluid, Kg/m3A= Projected area of body normal to direction of motion,m2V= Velocity of body, m/s2.2LiftLift force on a body may also be determined by the following equation:

When,FL= Lift force,NCL= Lift coefficient,Dimensonless= Density of fluid,kg/m3A= Projected area of body normal to lift vector,m2V= Velocity of the body,m/s

2.3Free Falling Of A Body In Liquid ColumnWhen a small ball is sinking in liquid, in the first duration that the ball is dropped the ball will move at accelerated rates because the forces acting on the ball is not yet in equilibrium. This accelaration will cause the ball to move down at higher velocity and against higher drag force. The drag force will be heigher until this acting force against the body is in an equilibrium state as shown in Figure 3 below.

The ball will move at constant velocity. Thus force acting on the ball by free falling in liquid column will be : FZ= W FB FD = m.a = 0................ (3)Where,W= Weight of the ball,NFB= Buoyant force of the ball,NFD= Drag force of the ball,NM= Mass of the ball,NA= Acceleration of the ball = 0kgThe buoyant force of the body can be determined by the following equation :FB=. VWhere,=Specific weight of the liquid,N/m3V=Volume of the body,m3Thus, from equation (3) givesFD= W - FBSubtitute FD from equation (1) in the above equation, giveIn case of the tree falling body in fluid at very low Reynolds number [(VD/)] < 1, where D is diameter of the spherical body, the flow is considered laminar of viscous flow, total drag can be determined by Stokes Law, i.e.FD = 3VDSubstitute this value FD in equation (2) and also substitute A = D2/4 then we getCD = 24/ReDThe value of CD of spherical body at very low Reynolds numbers may be obtained from the graph at left hand side of Figure 4.If the Reynolds number is increased beyond 1, the laminar boundary layer will separate from the surface of the spherical body, starting behind the point of zero velocity called stagnation point. At this point the pressure gradient is very high, which can be seen from Figure 4 that the curve of CD begins to deviate fro the horizontal axis as the drag force from the pressure is increased and the drag beconmes more proportional to V2. As the value of the Reynolds number increases further, the separation point where the boundary layer is separated from the surface will move forward on the sphere until, at the Reynolds numbers of about 1,000, the point of separation remains at an angle of about 80 degrees from the stagnation point.For a considered range og Reynolds numbers with stable condition, the laminar boundary layer with depart from the surface in the front half section of the sphere whereby the value of CD is rather constant at about 0.45. However,the value of CD of the mnooth sphere is decreased rapidly to about 50% when Reynolds number is about 250,000 as shown in Figure 4. This is because of the flow within the boundary layer changes from laminar flow to turbulent flow;point. Consequently it also result in a decrease in the size of the make and the pressure drag.

If the level og turbulence in free stream is high, the laminar boundary layer will transform to the turbulent bpundary layer at lower Reynolds numbers. Because of the change in position of the separation point is well defined, the sphere is thus often used as a turbulence indicator. For value of CD = 0,3, the Reynolads number which is in the middle range of the curve section on the left side of the graph in Figure 4 will be used for accurate measure of the turbulence.

3. TEST PROCEDURES 3.1Measure the diameter of the ball or the streamlined body.3.2Turn on the fluorescent lamp.3.3Fill in an oil of known viscosity into the glass tubes up to the operating level.3.4Measure the temperature of the oil for determination of density and releasing.3.5Drop the ball or the streamlined body through guide tube section for releasing.3.6Start timing for the movement of the ball (or the streamlined body) from the upper level mark to the lower level mark and record the time interval.3.7Repeat 3.5 and 3.6 many times to find an average velocity of the ball.Note:Viscosity of an oil can be obtained from the oil company.