Types of flow:

1.         Steady flow:(stream line flow)(laminar flow) the fluid flows in steady layers, any fluid particle follows a smooth path called stream line.

2.         The turbulent flow: when the velocity of flow exceeds a certain limit, it is characterized by small eddy circles.

The conditions of steady flow of a liquid through a tube:

1.      the liquid fills the tube completely.

2.      The quantity of the liquid which enters the tube from one end in a certain period of time is equal to that which leaves the other end at the same time.

3.      The velocity of an particle at a certain point during its flow is constant at any period of time(the velocity of flow should be less than the critical velocity).

  The stream line:

It is the imaginary line showing the path of a liquid particle during its flow.

it is imaginary line taken as measurement for the velocity or the rate of flow.

  The properties of the stream lines:

1.      They don’t intersect (do not cross over one another).

2.      They come closer together where the speed of the liquid is high & far a part where the speed is low.

3.      The tangent at any point of a stream line gives the direction of the instantaneous velocity of the liquid particle at that point.

The flow rate:

it is equal the mass of the fluid which enters or leaves the tube per unit time.

it is equal to the number of stream lines passing through a unit area which is perpendicular to the direction of flow.

Flow rate:

it is the volume of the fluid which enters or leaves the tube per unit time.

 Since, flow rate=v/t .

Q=v/t

Since, v=A/S                   S:the distance covered in 1 second.

Since,S=V.T                    v:the speed of the liquid.

Therefore, Q=A.S/t

Therefore, Q=Avt/t

Therefore, Q=AV   m^3/sec

Another method:

it is the mass of the fluid which enters or leaves the tube per unit time.

Since, the flow rate = volume of the fluid x density of the fluid    = V r / t 

Since, V = A.S
= A.S.r / t
Since, S = V.t
= A.V.t.r / t

\ Q = A.V. r