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Assignment 2

MECH 481: Aerodynamics of Aircraft

Due: Monday, Jan 30, 2017

Question 1. Air blows over the flat-bottomed, two-dimensional object shown in Figure. The shape of the

object, ( )xyy = , and the fluid speed along the surface, ( )xuu = , are given in the table. Determine the lift

coefficient using the Bernoulli equation.

����� = ��12 ���

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Question 2. Assuming that the flow is steady, the fluid is inviscid and

incompressible. Application of amFvr

= along and normal to the streamline results in

Bernoulli’s equation

Euler’s normal equation

This question illustrates a common misapplication of Bernoulli’s equation. Following figure shows two simple

flow fields called a free vortex and a forced vortex. The circumferential velocities in a free vortex and a forced

vortex, respectively, are

r

CV free = and ωrV forced =

In this case smC20.4= , srad0.1=ω , r is in meters, and V is in meters per second.

Apply Bernoulli’s equation and Euler’s normal equation between point A where mrA 0.2= and point B

where mrB 0.8= to calculate the pressure difference ( )AB pp − for both types of vortex. Both flows involve

Co20 water and lie in a horizontal plane

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Question 3. In some applications, elbow type flow meters like the one shown in Figure are used to

measure flow rates. The pipe radius is �, the radius of curvature of the elbow is �, and the pressure

difference ∆� across the curvature inside the pipe is measured. From the potential flow theory, it is known

that �� = �, where � is the fluid velocity at a distance � from the center of curvature �, and � is a constant.

Assuming frictionless steady-state flow and thus the Bernoulli equation across streamlines to be applicable,

obtain a relation for the volume flow rate as a function of , �, ∆�, �,and �.

� ��� − �� − � �� !� = " #� − ��� − ��$

%&'

%('

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Question 4. Professor Walter Tunnel needs to measure the flow velocity in a water tunnel. Due to

budgetary restrictions, he cannot afford a pitot-static tube, but instead he inserts a total-head probe and a

static-head probe, as shown, a distance )* apart from each other. Both probes are in the main free stream of

the water tunnel, unaffected by the thin boundary layers on the sidewalls. The two probes are connected to a

U-tube manometer. The densities and vertical distances are shown in Figure.

(a) Write an expression for velocity V in terms of the parameters in the problem.

(b) Is it critical that distance )* be measured accurately?