Question

Blood is flowing at the rate of $200{\mathrm{cm}}^3{\mathrm{s}}^{-1}$ in a capillary of a cross-section area$0.5{\mathrm{m}}^2$. The velocity of flow in $\mathrm{mm}{\mathrm{s}}^{-1}$ is

Answer 1

Step 1: Given data

Rate of flow of blood, $Q=200{\mathrm{cm}}^3{\mathrm{s}}^{-1}=200\times {10}^{-6}{\mathrm{m}}^3{\mathrm{s}}^{-1}$(constant)

Area of the cross-section of the tube, $\mathrm{a}=0.5{\mathrm{m}}^2$

Step 2: To find

We have to determine the velocity of flow.

Step 3: Calculation

Now using the equation of rate of flow of liquid in terms of the area and velocity is,

$Q=av$

$200\times {10}^{-6}=0.5v$

$$\begin{gathered} v=\frac{200\times {10}^{-6}}{0.5} \\ v=\frac{200\times {10}^{-6}}{5\times {10}^{-1}} \\ v=\frac{20\times {10}^{-4}}{5} \\ v=4\times {10}^{-4}\mathrm{m}{\mathrm{s}}^{-1} \\ v=0.4\mathrm{mm}{\mathrm{s}}^{-1} \end{gathered}$$

Hence, the velocity of the flow of blood is $0.4\mathrm{mm}{\mathrm{s}}^{-1}$.