Laminar flow, drag force

For laminar flow a similar differential force balance, balancing the drag force on a blade section and the torque can be formulated. For creeping flow inertial forces are not important and viscous forces completely dominates the flow. The laminar steady drag force on the fluid can be written as F a p,UD, where p, is the fluid viscosity. Substituting U with kND the power becomes P a pN D or = K, where K is the Newton number for laminar flow. K can be rewritten as ... 

If the drag force of the atmosphere is negligible, the retarding force for laminar flow is attributable to the viscous drag in the liquid at the distance v from the surface given by ... 

If a particle is moving in a fluid which is in laminar flow, the drag coefficient is approximately equal to that in a still fluid, provided that the local relative velocity at the particular location of the particle is used in the calculation of the drag force. When the velocity gradient is sufficiently large to give a significant variation of velocity across the diameter of the particle, however, the estimated force may be somewhat in error. 

For a rigid sphere on the axis of a tube through which a fluid moves in laminar flow (Fig. 9.1 with h = 0), Haberman and Sayre (HI) showed that the magnitude of the drag force is... 

Figure 11.3 is a plot of G(p) as a function of p for both prolate and oblate ellipsoids. This expression for the drag force is valid for both laminar and turbulent flow. For laminar flow the drag fort becomes... 

A particle settling in a centrifugal field is acted upon by a drag force and a centrifugal force. The force balance in the laminar flow region is given by ... 

Consider laminar flow of a fluid over a flat plate maintained at a constant temperature. Now the free-slreani velocity of the fluid is doubled. Determine the change in the drag force on the plate and rate of heat transfer between the fluid and tlie plate. Assume the flow to remain laminar. 

The advancement of a flow through the duct is accompanied by its deceleration near the walls and by the EPR drag force, thus displacing the liquid to the center of the duct. This leads to the surprising maxima on the longitudinal velocity profiles, Fig. 3.12. The flow in the middle constantly accelerates, but its value tends to a certain limit reached in the main steady-state region. For this laminar case, v = const, the dimensionless axial velocity is known to reach the value 1.5 irrespective to Re [380], if the EPR is absent. In the case of interest, it depends upon all the parameters A, 6, and Re, can be... 

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