Question

A Rankine oval is formed by combining a source-sink pair, each having a strength of 36 ft2/s and separated by a distance of 15 ft along the x axis, with a uniform velocity of 12 ft/s (in the positive x direction). Determine the length of the oval.

Answer 1

Answer:

0.28 ft

Explanation:

We are given that

Strength=m=$36ft^2/s$

Distance between source and sink=15 ft

Distance between the sink of the source and origin=$a=\frac{15}{2}$ ft

Uniform velocity, U=12 ft/s

We have to find the length of the oval.

Formula to find the half length of the body

$\frac{l}{a}=(\frac{m}{\pi Ua}+1)^{\frac{1}{2}}$

Where a=Distance between sink of source and origin

U=Uniform velocity

m=Strength

l=Half length

Using the formula

$\frac{l}{\frac{15}{2}}=(\frac{36}{\pi\times 12\times \frac{15}{2}}+1)^{\frac{1}{2}}$

$l=\frac{2}{15}(\frac{36}{\pi\times 12\times \frac{15}{2}}+1)^{\frac{1}{2}}$

$l=0.14$

Length of oval=$2l=2(0.14)=0.28 ft$