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Once the drag coefficient is available, the drag force acting on a body in cross flow can be determined from Eq. This behavior is characteristic of blunt bodies. transfernecia

Both the friction drag and the pressure drag can be sig- nificant. Therefore, the drag coefficient in this case is reduced by a fac- tor of 5 by simply roughening the surface. Cengell nature of the flow across a cylinder or sphere strongly affects the total drag coefficient CD. This results in a much smaller drag coefficient and thus drag force for a rough- surfaced cylinder or sphere in a certain range of Reynolds number compared to a smooth one of identical size at the same velocity.

The delay of separation in turbulent flow is caused by the rapid fluctuations of the fluid in the transverse direction, which enables the turbulent boundary layer to travel further along the surface before separation occurs, resulting in a narrower wake and a smaller pressure drag.

Transferencia De Calor Y Masa Cengel 4 Ed : Free Download, Borrow, and Streaming : Internet Archive

In the range of Reynolds numbers where the flow changes from laminar to turbulent, even the drag force FD decreases as the velocity and thus Reynolds number in- creases. It should be kept in mind that the free-stream turbulence and disturbances by other bodies in flow such as flow over tube bundles may affect the drag coefficients significantly.

This is in contrast to streamlined bodies, which experience an increase in the drag coefficient mostly due to friction drag when the boundary layer becomes turbulent. This results in a sudden decrease in drag of a flying body and insta- bilities in flight.


For a table tennis cenbel, however, the distances are very short, and the balls never reach the speeds in the turbulent range. At higher velocities, the fluid still hugs the cylinder on the frontal side, but it is too fast to remain attached to the surface as trxnsferencia approaches the top of the cylinder.

This is done by tripping the flow into turbulence at a lower Reynolds number, and thus causing the fluid to close in behind the body, narrowing the wake and reducing pressure drag considerably.

This large reduction in CD is due to the flow in the boundary layer becoming turbulent, which moves the separation point further on the rear of the body, reducing the size of the wake and thus the magnitude of the pressure drag. Both effects are significant at intermediate Reynolds numbers.

Cap 7 e 8 Cengel – Transferencia de calor e massa

The curves exhibit differ- ent behaviors in different ranges of Reynolds numbers: For blunt bodies such as a circular cylinder or sphere, however, an increase in the surface roughness may actually decrease the drag coefficient, as shown in Figure 7—19 for a sphere.

The drag force is transfersncia to the square of the velocity, and the increase in velocity at higher Reynolds numbers usually more than offsets the decrease in the drag coefficient. Obviously, roughening the sphere in this case will increase the drag by a factor of 4 Fig.

The average drag coefficients CD for cross flow over a smooth single circu- lar cylinder and a sphere are given in Figure 7— A decrease in the drag coefficient does not necessarily indicate a decrease in drag. At this point, the drag is mostly about 95 percent due to pressure drag.

The occurrence of turbulent flow at this Reynolds number reduces the drag coefficient of a golf ball by half, as shown in Figure 7— Experienced golfers also give the ball a spin during the hit, which helps the rough ball develop a lift and thus travel higher and further. This is especially the case for streamlined bodies.


There is no flow separation in this regime. For a given hit, this means a longer distance for the ball. Therefore, the surfaces of table tennis balls are made smooth.

Transferencia De Calor Y Masa Cengel 4 Ed

Thus, the fluid follows the curvature of the cylinder. A similar argument can be given for a tennis ball. The high pressure in the vicinity of the stagnation point and the low pressure on the opposite side in the wake produce a net force on the body in the direction of flow. The discussion above shows that roughening the surface can be used to great advantage in reducing drag, but it can also backfire on us if we are not careful—specifically, if we do not operate in the right range of Reynolds num- ber.

Assumptions 1 The outer surface of the pipe is smooth so that Figure 7—17 can be used to determine the drag coefficient. Enviado por Fernanda flag Denunciar. Flow in the wake region is characterized by random vortex formation and pressures much lower than the stagnation point pressure. As a result, the boundary layer detaches from the surface, forming a separation region behind the cylinder.

The drag force that acts on the pipe is to be determined.

The flow in the yunhs layer is laminar in this range, but the flow in the separated region past the cylinder or sphere is highly turbulent with a wide turbulent wake.