Aim

The aim of the experiment is to investigate the variations of the coefficient drag of a cylinder

with increasing velocity.

Theory

The drag of an object subjected to a flow can be calculated using the following equation:

Fw=½pCwAu²

Drag increases with the square of the velocity. A is the area of the model/

Where:

Fw: the force of drag,

ρ: the density of the fluid

u: the velocity of the object relative to the fluid

A: reference area

Cw: the drag coefficient , a dimensionless constant Furthermore, it is governed by the density p of the air, the projected area A of the object and

the drag coefficient Cw, which reflects the influence of the object’s shape, but is independent of

its size. If Cw is known, then drag can be calculated in advance for any body. The drag

coefficient can be determined from the drag at a given velocity.

Cw = 2Fw/pAu2

A cylinder is installed in the measurement section at right angles to the direction of flow and

the drag force measured at increasing velocities.

Procedure

1) Measure ambient pressure and temperature and deduce the local air density from the ideal

gas law. Also deduce the ambient viscosity using the Sutherland correlation.

2) Measure length and diameter of the cylinder and calculate the projected area of the cylinder

3) Mount model on force transducer and close wind tunnel properly

4) Start wind tunnel at low onset velocity

5) Measure speed

6) Using both anemometer and data acquisition system record value of the drag force

7) Repeat 5 and 6 for onset velocities up to 25m/s (take at least 10 readings)

8) Calculate Cw values using equation (2).

9) Plot graph of Cw vs Reynolds number (Re)

Results Table

Velocity (m/s)

Drag Force(N)

Area (m²)

Density(ρ) Viscosity(μ) Drag Coefficient

(Cw) Reynolds

Number(Re)

0 0

0.0157 1.19 1.87

0.000 0

5 0.01 0.043 15909.091

8 0.11 0.184 25454.545

12 0.26 0.193 38181.818

16 0.52 0.217 50909.091

20 0.89 0.238 63636.364

22 1.01 0.223 70000

26 1.32 0.209 82727.273

For this experiment the velocity range is from 0 to 26 m/s, then we read the drag force at each

velocity. Diameter and Length of the cylinder were 5cm and 10cm , which we must convert to

meter (m).

Temperature (K) = 23 + 273 = 296 K Pressure= 101488 Pa. Specific heat Capacity= 287 ⁄

Calculations

Sample used for the calculation section was done e using velocity 16 m/s, please check the table above.

Area of the Cylinder:

( )( ) ( )( )

Density of Air:

( )( )

( ⁄ )( )

⁄

Viscosity of Air:

( ( ))

kg/ms

Drag Coefficient Cw:

( )

( )( ) ( )

( )

( ⁄ )( ) ( )

Reynolds Number:

( )⁄ ( ) ( )

38181.818

Graphs The graph below shows Drag coefficient vs Reynolds number.

0.000

0.050

0.100

0.150

0.200

0.250

0 10000 20000 30000 40000 50000 60000 70000 80000 90000

Cw

Re

Cw VS Re

Discussion We can see from the graph that as the Cw increases , Reynolds number increases as too,

therefore Cw is proportional to Re.

Reynolds number Re is a dimensionless number used to determine if flow is laminar, transient or

turbulent. For our experiment Reynolds number for the cylinder is from 0 to 82727.

It is important to note that for our calculation for the 12 m/s the resultant Reynolds number

was 38181.818 which mean its less than 4000, therefore its in the transient state.

Cw is a dimensionless number used to quantify the drag or resistance of a body in a fluid

environment. Any type of body traveling through a fluid will experience drag or resistance, the

net force in the direction of flow due to pressure and shear stress forces on the surface of the

body. Cw is a function of several factors including shape of the body, Reynolds Number for the

flow, Roughness of the Surface.

Turbulent flow is caused by high velocities which leads to flow with highly disordered motion.

We assume that flow becomes turbulent when the velocity of the fluid increases, the Cw

increases too. This assumption is correct which is shown by the calculation we did.

Conclusion Velocity is proportional to Fw, when the velocity increases the drag force increases. Cw

increases as the Fw increases therefore they are proportional. However this is not true for the

last two readings in the table, if you look at the section for velocity 22 and 26 m/s, we can see

that even when Fw increases Cw decreases. Maybe this is due to calculations or equipment

problems. Velocity is proportional to Reynolds number, increasing the velocity will make the

flow more turbulent.