Blood is flowing at the rates of 200 `cm^(3)//sec` in a capillary of cross-sectional area `0.5m^(2)`. The velocity of flow, (in mm/sec) is:

Options

A. 0.1
B. 0.2
C. 0.3
D. 0.4

Answer

To find the velocity of blood flow in the capillary, we can use the relationship between flow rate, cross-sectional area, and velocity. The formula we will use is:

\[ Q = A \cdot v \]

where:
- \( Q \) is the flow rate (in cubic meters per second),
- \( A \) is the cross-sectional area (in square meters),
- \( v \) is the velocity of flow (in meters per second).

### Step 1: Convert the flow rate from cm³/sec to m³/sec

Given:
- Flow rate \( Q = 200 \, \text{cm}^3/\text{sec} \)

To convert cm³ to m³, we use the conversion factor:
\[ 1 \, \text{cm}^3 = 10^{-6} \, \text{m}^3 \]

So,
\[ Q = 200 \, \text{cm}^3/\text{sec} \times 10^{-6} \, \text{m}^3/\text{cm}^3 = 200 \times 10^{-6} \, \text{m}^3/\text{sec} = 0.0002 \, \text{m}^3/\text{sec} \]

### Step 2: Use the formula to find the velocity

Now, we have:
- \( Q = 0.0002 \, \text{m}^3/\text{sec} \)
- \( A = 0.5 \, \text{m}^2 \)

We can rearrange the formula to solve for \( v \):
\[ v = \frac{Q}{A} \]

Substituting the values:
\[ v = \frac{0.0002 \, \text{m}^3/\text{sec}}{0.5 \, \text{m}^2} \]

Calculating \( v \):
\[ v = 0.0004 \, \text{m/sec} \]

### Step 3: Convert the velocity from m/sec to mm/sec

To convert meters per second to millimeters per second, we use the conversion factor:
\[ 1 \, \text{m} = 1000 \, \text{mm} \]

Thus,
\[ v = 0.0004 \, \text{m/sec} \times 1000 \, \text{mm/m} = 0.4 \, \text{mm/sec} \]

### Final Answer

The velocity of the flow is:
\[ \boxed{0.4 \, \text{mm/sec}} \]

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