The flow of blood in a large artery of an anesthetised dog is diverted through a venturimeter. The wider part of the meter has a cross-sectional area equal to that of the artery, `A=16 mm^(2)`. The narrower part has an area `a=9mm^(2)`. The pressure drop in the artery is 24 Pa. What is the speed of the blood in the artery ?

Explanation

Bernoulli's equation for the horizontal flow of blood is
`p_(1)+(1)/(2)rho v_(1)^(2)=p_(2)+(1)/(2)rho v_(2)^(2)`
By equation of continuity,
`Av_(1)=av_(2) " or " v_(2)=Av_(1)//a`
`therefore p_(1)-p_(2)=(1)/(2)=(1)/(2)(rho A^(2)v_(1)^(2))/(a^(2))-(1)/(2) rhov_(1)^(2)=(1)/(2)rho v_(1)^(2)[(A^(2))/(a^(2))-1]`
Here, `p_(1)-p_(2)=24 Pa`
`rho ("blood")=1.06xx10^(3) kg m^(-3), A//a=16//8=2`
` therefore v_(1)=sqrt((2(p_(1)-p_(2)))/(rho((A^(2)-1)/(a^(2)))))=sqrt((2xx24)/1.06xx10^(3)xx(2^(2)-1))=0.125 ms^(-1)`