Gas with density $$ flows through a two$-$

dimensional elbow as shown in the figure. The

elbow is in a horizontal plane, so the pressure

difference between the two pressure taps due to

the earth's gravitational acceleration can be

ignored. A U$-$manometer is connected between

two pressure taps and contains a liquid with a

density of ${}_1.$ Assuming the velocity distribution

in the cross section between the pressure holes is

constant, V$.$ Obtain expressions for Vin terms of

$,{}_1,h,R_0,$ and $R_4$ and other appropriate

parameters.

$40\%$