Question

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, i.e. $10m{m}^2$ . The narrower part has an area $5m{m}^2$ . The pressure drop in the artery is $22Pa$ . (Take the density of the blood $=1.06\times 10^{3}kg{m}^{-3}$ . The speed of the blood in the artery is

• A. $0.12m{s}^{-1}$
• B. $0.62m{s}^{-1}$
• C. $0.24m{s}^{-1}$
• D. $0.42m{s}^{-1}$

Answer 1

Answer: (A)

Here, $A=10m{m}^2$ , $a-5m{m}^2$ ,
$\rho =1.06\times 10^{3}kg{m}^{-3}=1060kg{m}^{-3},P_1-P_2=22Pa$
Speed of the fluid through the wide neck is
$v=\sqrt{\frac{2\left(P_1-P_2\right)}{\rho }}{\left\{{\left(\frac{A}{a}\right)}^2-1\right\}}^{-1/2}$
or $\frac{A}{a}=\frac{10}{5}=2$
$\therefore v=\sqrt{\frac{2\times 22}{1060\left(2^2-1\right)}}$
$=0.12m{s}^{-1}$