First slide

Fluid dynamics

Question

The flow of blood in a large artery of a anesthetized dog is diverted through a ventruimeter. The wider part of the meter has a cross-sectional area equal to that of the artery, i.e., 10 ${mm}^{2} . The narrower part has an area 5 {mm}^{2} .$ The pressure drop in the artery is 22 pa. Density of the blood is $1.06 \times 10^{3} kg m^{- 3}$ . The speed of the blood in the artery is

Moderate

A

0.12 $m s^{- 1}$
B

0.62 $m s^{- 1}$
C

0.24 $m s^{- 1}$
D

0.42 $m s^{- 1}$

Solution

Here,
A = 10 ${mm}^{2}$ , a = 5 ${mm}^{2}$ , $ρ = 1.06 \times 10^{2} kg m^{- 3}$
= 1060 $k g m^{- 3}, P_{1} - P_{2} = 22 P a$
Speed of the fluid through the wide neck is
v = $\sqrt{\frac{2 (P_{1} - P_{2})}{ρ}} {{(\frac{A}{a})}^{2} - 1}^{\frac{- 1}{2}}$
or $\frac{A}{a} = \frac{10}{5} = 2$
v = $\sqrt{\frac{2 \times 22}{1060 (2^{2} - 1)}} = 0.12 {ms}^{- 1}$

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