力学作业（英文版）- (13).pdf

Problem Set 3B Name: ____________________

Assigned: Thursday, September 20
Due: Tuesday, September 25


1. Consider an airfoil where the flow over the foil is two-dimensional (this is the same as
assuming the foil is infinitely long in the z-direction, out of the page). We want to find
the drag force D in the x-direction on a section of the foil having width w in the z-
direction. Assume the following for the figure shown:

• The velocity profile at a downstream location is known and is u(y)
• The flow is steady and symmetric around the foil (the foil is not inclined to the
flow)
• The front and rear surfaces of the control volume shown is chosen to be at large
distances up and downstream from the foil so that the pressure is atmospheric
• The value of h is chosen large enough so that the ponent of the air velocity
v
Vuv= (,) at the top and bottom surfaces of the control volume is approximately
the same as the “free-stream” velocity U ∞.

m& top




y h

D u(y)
x



U ∞



m rear
front & bottom


(a) First, use the conservation of momentum for a fixed control volume to write an
expression for the total force on the fluid in the control volume in terms of surface
integrals over the front, rear, top and bottom surfaces of the control volume. Note that by
assumption of 2-D fl