Question

In a streamline (laminar flow) the velocity of flow at any point in the liquid:
A) Does not vary with time
B) May vary in direction but not in magnitude
C) May vary in magnitude but not in the direction
D) May vary both in magnitude and direction

Answer 1

Hint: In streamline flow fluids flow in parallel layers such that there is no disruption or intermixing of the layer at a given point so by definition, In streamline flow, the velocity of flow at any chosen point in the liquid is always the same i.e. doesn’t vary with time either in magnitude or in direction.

Complete step by step answer:
The velocity of a liquid at a point remains constant in time. above a certain critical speed, the fluid flow becomes unsteady this irregular flow is called critical velocity or turbulent flow

Continuity equation for ideal liquids,
Let \[{a_1}{v_1} = {a_2}{v_2} = {a_3}{v_3}\] \[{a_1}{a_2}{a_3}\] be the area of cross section area of the tube and \[{v_1}{v_2}{v_3}\] be the velocities respectively then,
 \[{a_1}{v_1} = {a_2}{v_2} = {a_3}{v_3}\]
Here, it is clear that the velocity of flow of liquid is inversely proportional to the area of cross section. Velocity is small at those points where the area of the cross section is large and vice-versa.

Therefore we can say in laminar flow velocity does not change with time. So, option (A) is correct.

Note:
The velocity of a fluid at a point remains constant but above critical speed or turbulent flow the fluids become unsteady In Bernoulli’s principle equation of continuity is used.
Bernoulli principle - If a small amount of non-viscous, incompressible liquid flows from one point to another its total energy remains constant throughout the displacement.