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 ?

Options

A. `0.135 ms^(-1)`
B. `0.095ms^(-1)`
C. `0.0125ms^(-1)`
D. `0.1125 ms^(-1)`

Answer

B

Explanation

Bernoulli's theorem for the horizontal flow of blood is
`p_1+1/2rhov_1^2 = p_2+1/2rhov_2^2`
BY equation of continuity
`Av_1 = av_2 " or " v_2Av_1//a`
`therefore p_1-p_2 = 1/2 (rhoA^2v_1^2)/(a^2)-1/2rhov_1^2 = 1/2rhov_1^2[A^2/a^2-1]`
Here `p_1 - p_2 = 24Pa`
`rho("blood") = 1.06xx10^3 kgm^(-3), A//a=16//8=2`
`therfore v_1sqrt((2(p_1-p_2))/(rhoA^2/a^2-a))`
`=sqrt((2xx24)/(1.06xx10^3xx(2^2-1))=0.095ms^(-1)`