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This is especially the case for streamlined bodies. Both the friction drag and the pressure drag can be sig- nificant.

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. For a given hit, this means a longer distance for the ball. Therefore, the surfaces of table tennis balls are made smooth. The drag force that acts on the pipe is to be determined. This is in contrast to streamlined bodies, which experience an increase in the drag coefficient mostly due to friction drag cengrl the boundary layer becomes turbulent.

Effect of Surface Roughness We mentioned earlier that surface roughness, in general, increases the drag coefficient in turbulent flow. The drag force is proportional 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.

Cap 7 e 8 Cengel – Transferencia de calor e massa

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.

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.


The nature of the flow across a cylinder or sphere strongly affects the total drag coefficient CD.

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 transfeencia the drag coefficients significantly.

The high pressure in the vicinity of the stagnation calr and the low pressure on the opposite side in the wake produce a net force on the body in the direction of flow.

Therefore, the drag coefficient in this case is reduced by a fac- tor of 5 by simply roughening the surface. This results in a much smaller drag yunu 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.

Assumptions 1 The outer surface of the pipe is smooth so that Figure 7—17 can be used to determine the drag coefficient.

Mecanica de Fluidos Fundamentos y Aplicaciones – Yunus Cengel by Yunus A. Cengel – PDF Drive

The occurrence of turbulent flow at this Reynolds number reduces the drag coefficient of a golf ball by half, as shown in Figure 7— This is done by tripping the flow into turbulence at a lower Reynolds number, and thus causing the transferecnia to close in behind the body, narrowing the wake and reducing pressure drag considerably.

There is no flow separation in this regime. The average drag coefficients CD for cegel flow tunus a smooth tansferencia circu- lar cylinder and a sphere are given in Figure 7— This behavior is characteristic of blunt bodies.

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. Thus, the fluid follows the curvature of the cylinder. The curves exhibit differ- ent behaviors in different ranges of Reynolds numbers: Obviously, roughening the sphere in this case will increase the drag by a factor of 4 Fig.


For a table tennis ball, however, the distances are very short, and the balls never reach the speeds in the turbulent range. As a result, the boundary layer detaches from the surface, forming a separation region behind the cylinder. Flow in the wake region is characterized by random vortex formation and pressures much lower than the stagnation point pressure. Once the drag coefficient is available, the drag force acting on a body in cross flow can be determined from Eq. At higher velocities, the fluid still hugs the cylinder on the frontal side, but it is too fast to remain attached cengle the surface as it approaches the top of the yunuus.

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

A decrease in the drag coefficient does not necessarily indicate a decrease in drag. This results in a sudden calog in drag of a flying body and insta- bilities in flight.

A similar argument can be given for a tennis ball. At this point, the drag is mostly about 95 percent due to pressure drag.

The transferencai in the boundary 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.

Enviado por Fernanda flag Denunciar. Both effects are significant at intermediate Reynolds numbers.