54
2 Water at Rest and in Motion
Sometimes drag force, Fx , is expressed per unit length of cylinder, i.e.:
(2.63)
where D = 2a, the diameter of the cylinder.
Equation (2.62) provides a basic framework for the experimental determination of a drag coefficient Cd because:
(2.64)
The drag force, developed above, was based on the assumption that at some
point on a cylinder the flow separates, deviating from the path it would have
taken if the fluid was ideal. The overall drag of a body is usually separated
into two components, pressure drag and friction drag. Pressure drag is a consequence of the difference between the high pressure of the front stagnation
region, and the low pressure of the rear separated region. For streamlined bodies (for example, fish), the flow is less likely to separate and streamlined bodies
cause very little disturbance to the flow. Therefore, it is reasonable to assume
that almost total drag is due to shear stress in the boundary layer over the
body. This type of drag is known as friction drag.
Let us examine friction drag for a thin plate. For simplicity, we will consider
a two-dimensional plate of length L (in flow direction) and width b. Because of
the non-slip condition (see Sect. 2.5.2), the fluid flowing very close to the plate
is retarded to form a boundary layer and some force is needed to establish the
velocity gradient. The drag due to friction is given by (Schlichting, 1960):
(2.65)
where Sw is the total wetted area ,of the plate (equal to bL), Uo is the mainstream
velocity, and Cd, friction is the frictional drag coefficient. The value of Cd,friction
depends on the boundary layer flow regime, and for the laminar boundary layer,
with Reynolds number greater than 10 6 , we have (Schlichting, 1960):
1.33
Cd, friction = ,j'Re'
(2.66)
and for turbulent flow:
0.072
C d,friction = ReO.2 ·
(2.67)
2 Water at Rest and in Motion
Sometimes drag force, Fx , is expressed per unit length of cylinder, i.e.:
(2.63)
where D = 2a, the diameter of the cylinder.
Equation (2.62) provides a basic framework for the experimental determination of a drag coefficient Cd because:
(2.64)
The drag force, developed above, was based on the assumption that at some
point on a cylinder the flow separates, deviating from the path it would have
taken if the fluid was ideal. The overall drag of a body is usually separated
into two components, pressure drag and friction drag. Pressure drag is a consequence of the difference between the high pressure of the front stagnation
region, and the low pressure of the rear separated region. For streamlined bodies (for example, fish), the flow is less likely to separate and streamlined bodies
cause very little disturbance to the flow. Therefore, it is reasonable to assume
that almost total drag is due to shear stress in the boundary layer over the
body. This type of drag is known as friction drag.
Let us examine friction drag for a thin plate. For simplicity, we will consider
a two-dimensional plate of length L (in flow direction) and width b. Because of
the non-slip condition (see Sect. 2.5.2), the fluid flowing very close to the plate
is retarded to form a boundary layer and some force is needed to establish the
velocity gradient. The drag due to friction is given by (Schlichting, 1960):
(2.65)
where Sw is the total wetted area ,of the plate (equal to bL), Uo is the mainstream
velocity, and Cd, friction is the frictional drag coefficient. The value of Cd,friction
depends on the boundary layer flow regime, and for the laminar boundary layer,
with Reynolds number greater than 10 6 , we have (Schlichting, 1960):
1.33
Cd, friction = ,j'Re'
(2.66)
and for turbulent flow:
0.072
C d,friction = ReO.2 ·
(2.67)