Introduction and Theoretical Background
The purpose of this lab is to show that pressure distribution along a frontal area expressed
in dimensionless terms is constant with varying velocity. This is proven by measuring
velocity and pressure distributions upstream, around, and in the wake of a cylinder in a
wind tunnel. After this data is obtained, the integral equations for mass and momentum
are used to estimate the drag on the cylinder.
The "drag coefficient", C
D
, will be used to convert drag force to dimensionless terms. The
equation for C
D
is:
C
D
= F
D
/(1/2ρA(V
2
))
For 24.382 m/s The Reynolds Number is 3.1656 x 10
4
(Calculation show in Figure 1)
C
D
~1.5 (from figure 2 in lab handout)
C
D
=1.50758 (from Figure 1 in lab writeup)
Where F
D
is drag force around the cylinder, ρ is the density of air, V is the velocity of the
air, and A is the frontal area of the cylinder. The denominator is the dynamic pressure
acting on the frontal area of the cylinder, and the numerator is the drag force or net force
in the streamwise direction (in our case, the xdirection). The drag force can be
determined by integrating the xcomponent of the pressure force around the cylinder:
F
D
= 2πDL/360∫Pcosθdθ
From 0 degrees to 180 degrees, where D and L are the diameter and length of the
cylinder, respectively, and Pcosθ is the xcomponent of the pressure around the cylinder.
The integration is from 0 to 180 degrees because the flow about the whole cylinder is
assumed symmetric. The integral cannot just be solved as it is because every angle would
have to be measured. Instead a trapezoidal approximation will have to be used to
approximate the integral in increments of 10 degrees. Also the boundary layer will have
to be extrapolated so that the calculations represent a uniform profile. The pressure
around the cylinder is expected to decrease until just before 90 degrees. This is because
the mass flow between any two stream lines is a constant since the density and mass flow
are the same; thus as the area between two streamlines goes down (from 0 to 90 degrees),
the velocity must increase. At just before 90 degrees gage static pressure is at its lowest
eg. 971Pa, this static pressure is what is causing the air to move there for when the gage
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 Spring '08
 FredThomas
 Fluid Dynamics, Drag force

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