Question
- Define streamline.
- Write any two properties of streamlines.
- Draw streamlines for a clockwise spinning sphere.
- Derive equation of continuity.
✓
Answer
- Streamline is the actual path followed by the procession of particles in a steady flow, which may be straight or curved such that tangent to it at any point indicates the direction of flow of a liquid at that point.
- Two properties of streamlines are-
- Two streamlines can never cross each other.
- The greater is the crowding of streamlines at a place, the greater will be the velocity of liquid particles at that place and vice-versa.
Due to spinning sphere, concentric streamlines are formed.
Volume of liquid entering per second at $A = a_1v_1$
Mass of liquid entering per second at $A = a_1v_1p_1$
Similarly, mass of liquid leaving per second at $B = a_2v_2p_2$
If there is no loss of liquid in tube and the flow is steady then,
Mass of liquid entering per second at A = Mass of liquid leaving per second at B $a_1v_1p_1 = a_2v_2p_2$
If liquid is incompressible then,
$P_1 = P_2$
$a_1v_1 = a_2v_2$
av = constant
This is the equation of continuity.
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