The flow of blood in a large artery of a anesthetized dog is diverted through a venturimeter. The wider part of the meter has a cross-sectional area equal to that of the artery. Ie., `10mm^(2)` . The narrower part has an area `5 mm^(2)`. The pressure drop in the artery is `22 Pa`. Density of the blood pressure drop in the artery is `22Pa`. Density of the blood pressure drop in the artery is `22Pa`. Density of the blood is `1.06xx10^(3)kgm^(-3)`. The speed of the blood in the artery is

Options

A. `0.12 m s^(-1)`
B. `0.62 m s^(-1)`
C. `0.24 m s^(-1)`
D. `0.42 m s^(-1)`

Answer

A

Explanation

Here, A=10 `"mm"^(2), a=5 "mm"^(2),`
`rho=1.06xx10^(3)kg m^(-3)=1060 kg m^(-3), P_(1)-P_(2)=22 Pa`
Speed of the fluid through the wide neck is
`v=sqrt((2(P_(1)-P_(2)))/(rho)){((A)/(a))^(2)-1}^(-1//2)` or `(A)/(a)=(10)/(5)=2`
`therefore v=sqrt((2xx22)/(1060(2^(2)-1)))=0.12 m s^(-1)`