Physics · Mechanical Properties Of Fluids · NEET
Av is the volume of fluid crossing a section each second (called volume flow rate). In steady flow no fluid piles up and none disappears, so the volume entering per second must equal the volume leaving per second. Speed alone can change and area alone can change, but their product Av must stay fixed. That is why we write A1 v1 = A2 v2.
Because Av = constant. If the area A gets smaller, the speed v must get larger to keep the product the same. The same amount of water has to squeeze through a smaller opening each second, so it must move quicker. This is exactly why pinching a hose makes the jet faster.
Yes. For an incompressible fluid the density is constant, so conserving mass is the same as conserving volume. Mass entering per second = density x A1 v1 and mass leaving per second = density x A2 v2. The density cancels, leaving A1 v1 = A2 v2. So continuity is conservation of mass written for fluid flow.
The simple form A1 v1 = A2 v2 works only when density does not change, so it is exact for liquids (incompressible) and fine for gases moving slowly. If a gas is compressed and its density changes, you must use the full form: density1 x A1 v1 = density2 x A2 v2. NEET fluid problems assume incompressible flow, so use Av = constant.
Speed v (m/s) tells how fast a fluid particle moves. Volume flow rate Q = Av (cubic metre per second) tells how much fluid passes a point each second. Continuity keeps Q the same along the pipe, but the speed v changes from place to place because the area A changes.
Water flows in streamline motion through a horizontal pipe of circular cross-section. The pressure difference of water between P and Q is 15 N/m2. The areas of cross-section at P and Q are 40 cm2 and 20 cm2 respectively. The rate of flow of water through the pipe (in cm3/s) is: (density of water = 1000 kg/m3)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For an incompressible fluid in steady flow, A1 v1 = A2 v2, meaning the volume flow rate Av is the same at every cross-section of the pipe.
Av is the volume flow rate, the volume of fluid passing through a cross-section each second, measured in cubic metre per second.
It is based on conservation of mass. For an incompressible fluid this becomes conservation of volume, giving Av = constant.
The speed doubles. Since Av must stay constant, halving the area forces the speed to become twice as large.
If they crossed, a fluid particle at that point could move in two directions at once, so the flow would not be steady. In steady flow each point has one fixed velocity.
