Question

V VISCOUS FLOWS Page 38 nar flow between two infinite plates a distance h apart driven by a pressure gra- Va20. For lami dient, the velocity profile is [constant] [linear] [parabolic] [hyperbolic] [elliptic] [error func- tion], and the flow rate Q is proportional to h to the power is driven by the top plate moving at a speed U in the absence of any pressure gradient, the velocity profile is [constant] linearl Iparabolic] [hyperbolic] [elliptic] [error function], and the flow rate Q is proportional to h to the power Va21. If instead of the exact solution for steady laminar flow Uo over a flat plate with distance measured from the leading edge, we assume an approximate profile given by u(y; r)/Uo-y() for y S (x) and by u(y; z)/Uo-1 for y 2 6(x); in terms of 6, the displacement thickness is given by 6 the wall shear stress by To If the flow the momentum thickness by 0 an The dependence of 6 on z is expected to be and 6y** ; also 6 U** 82** Va22. The apparent increase in the diffusivity of momentum due to turbulent fluctuations (u) is given the name general, for turbulent flows, this effect is Igreater than] (comparable tol [smaller thanj that due to viscosity except in a small region near the body called the Va23. In a turbulent flow, the rate of kinetic energy loss (per unit mass) e ((v2)/ôt) depends (ultimately) on the kinematic viscosity of the fluid v. Using dimensional analysis, the say diameter) n of the typical eddy responsible for this viscous dissipation is given in terms of e and v by n~ Similarly, the typical velocity vn of In which is given by the formula (η is the so-called Kolmogorov turbulent length scale). that eddy can be obtained in terms of e and v to be Va24. A shear flou givon turhulent with velocity fluctua-

please solve (va20) for me thanks!! :)

Answer 1

v a) 20) in a laminar flow between parallel plates

Q = Gh^3 / 12 $\mu$

so it is proportional to power 3

if it is driven by speed U

Q = Gh^3 / 12$\mu$ + 1/2 Uh

it is proportional to power h and h3