Chapter 10, Problem 35P

To determine

The average speed of flow in the major arteries of the body is to be calculated.

Answer to Problem 35P

The average speed of the blood flow is $0.9m/\sec$ .

Explanation of Solution

Given info:

The total cross-sectional area, $A=2.0c{m}^2=2\times {10}^{-4}{m}^2$

The radius of aorta, $r=1.2cm=0.012m$

Area of the aorta, $A_{aorta}=\pi r^2=3.14{\left(0.012\right)}^2=4.5\times {10}^{-4}{m}^2$

Speed, $v_1=40cm=0.4m$

Formula used:

The equation of continuity as,

  $\begin{array}{l}Av=constt\\ A_1{v}_1=A_2{v}_2\end{array}$

Calculation:

Now substitute the given values in the formula then the result is,

  $A_1{v}_1=A_{total}{v}_{avrage}$

  $v_{avrage}=\frac{A_1{v}_1}{A_{total}}=\frac{4.5\times {10}^{-4}{m}^2\times 0.4m/\sec }{2\times {10}^{-4}{m}^2}=0.9m/\sec$

Conclusion:

The average speed of the blood flow is $0.9m/\sec$ .