Question

The total area of the cross section is\[0.25{m^2}\] . If blood is flowing at the rate of\[100c{m^3}{s^{ - 1}}\], then the average velocity of flow of blood through the capillary, in \[mm{s^{ - 1}}\] is:
$A)0.4$
$B)4$
$C)25$
$D)400$

Answer 1

Hint: First we have to define what the terms we need to solve the problem are. Velocity is the vector quantity that measures displacement over the time. Average velocity of flow of blood through the capillary is flow rate of blood divides total area of cross section. One centimeter is a hundred meters. And one centimeter is ten millimeters.

Complete step by step answer:
In the given question we change all the given values as meters and since 100 centimeters equal to 1 meter or one centimeter equal to one-hundredth ($\dfrac{1}{{100}}$)meter.
Hence the flow rate of blood $ = 100c{m^3}{s^{ - 1}}$$ = 100 \times {10^3}m{m^3}{s^{ - 1}}$
When a solid object is intersected by a plane, an area is projected onto the plane.
Hence total area of cross section $ = 0.25{m^2}$and applying the above equation we get
Total is of cross section $ = 0.25{m^2}$$ = 0.25 \times {10^6}m{m^2}$
The average velocity of an object is total displacement divided by the total time taken. The SI unit is meters per second.
Hence the average velocity of blood through capillaries is $\dfrac{{flow{\text{ }}rate{\text{ }}of{\text{ }}blood}}{{total{\text{ }}area}}$$ = \dfrac{{{{10}^5}}}{{{{10}^6} \times 0.25}}mm{s^{ - 1}}$
Simplifying the above equation which is ten power five divides ten power six and hence we get
$ \Rightarrow \dfrac{1}{{10 \times 0.25}}mm{s^{ - 1}}$ (Now multiply by 10 so then it turns into 2.5)
$ \Rightarrow \dfrac{1}{{2.5}}mm{s^{ - 1}}$ Hence option A is correct and since option A is the only correct option, we cannot able to find any other possible ways like $4,25,400$(except calculation mistake).
Therefore, at finally we get average velocity of flow of blood through the capillary is $0.4mm{s^{ - 1}}$
So, the correct answer is “Option A”.

Note: Velocity is the vector quantity that measures displacement over the time. Average velocity of flow of blood through the capillary is flow rate of blood divides total area of cross section.One centimeter is hundred meters. And one centimeter is ten millimeters.