Test: Equation of Continuity - JEE MCQ

From the equation of continuity (av = constant), we have
0.5 V = 200 X 10^-6
V = 4 X 10^-4 m/s
V = 0.4 mm/s.

Streamline and turbulent flow. When the flow of liquid is such that the velocity, v of every particle at any point of the fluid is constant then the flow is said to be steady or streamline flow. The path followed by a particle of the fluid in stream-line flow is called steady or streamline flow.

Streamline flow is the characteristic that determines how water of a stream will move in the stream channel.

The word lamellar literally means line the fluid flows in lines when we see an ideal fluid, each particle follows a fixed line and there are numerous of this type in each layer so they don't lag each other.

In case of flowing fluids: product of pressure at any cross-section of pipe (in which fluid is flowing) and area of cross-section is constant. So, (PA) at source = (PA) at exit point and as we know that the cross section of the jet is less than the source (fire hydrant) => pressure at exit point (just outside jet) will be greater resulting more velocity of water at exit point. This way water can cover large distance so fire fighters can maintain a safe distance with fire.
Option B seems correct at first but in a closed pipe amount of water in will always be equal to amount of water out for any interval (considering a solid pipe) as option B is incorrect. Now option A should also be incorrect
As Mass = density × volume.

The equation of continuity for incompressible fluids states that the product of speed and cross-sectional area is always a constant. If a river becomes much deeper, the cross-sectional area becomes large and so the speed of flow is reduced. This is the origin of the expression “still waters run deep”.

Because equation of continuity depends on mass and equation of continuity play a major role in mass.

In case of streamlined flow of liquid, the loss of energy is minimum because different layers glide over one another without intermixing. Therefore, there is no collision between the molecules of different layers, and hence minimum energy loss.

We know by the conservation of volume we get that
0.3 L/sec =  150 x 0.02 cm² x v
Where v is the speed of the spray,
And we know 1L = 1 cm³
Hence we get v = 150 x 0.02 cm² /  .3 cm³/s
= 100 cm²/s