The equation of continuity:

Suppose two planes.

The cross sectional area of the first plane is A1.

The cross sectional area of the second plane is A2.

The volume of the liquid flowing through the area A1 per unit time is:

Q1 = A1.V1

The volume of the liquid flowing through the area A2 per unit time is:

Q2 = A2.V2

The motion of liquid is steady.

Q1 = Q2

A1.V1 = A2.V2

A1/A2 = V2/V1                                   
\ V a 1/A

V1/V2 = A2/A1 = p(r2)^2 / p(r1)^1  
\ V a 1/r^2

The fluid speed at any point in the tube is inversely proportional to the cross sectional area of the tube at that point. The liquid will flow very slowly when the cross sectional area is large & quickly if it is small.

OR

In the steady flow:

The flow rate entering the tube = The flow rate leaving the tube.

Q1 = Q2

A1.S1 = A2.S2

Since (S) is the distance covered in one second.

\ V = S/t

\ S = V

\ A1.V1 = A2.V2

\ A1/A2 = V2/V1                          

\ A a 1/V                         

The rule of branching tube:

A1.V1=A2.V2XN

N :no. of tubes

Example:

the cross-sectional area of the total capillaries is greater than that of the artery.

the blood flow velocity decreases in capillaries and this allows the exchange of gases and food in cells ,prevents the explosion of capillaries.