what is the relationship between density , area and velocity in fluid mechanics ? Does the relationship differs in the case of fluid dynamics.
Answers
Answer:
Hey mate your answer is here
Explanation:
Velocity and Pressure are inversely proportional to the Area of cross section of the body through which a fluid is flowing.
consider figure 1: An ideal fluid(that does not has viscosity(friction) among its particles ) flows through the pipe.
Lets consider the part AB of this pipe.We can say that the particle leaving the pipe in 1 second is equal to particle entering the pipe in 1 second.
Lets assume 10 particles can enter at a time through A at once and only and only 2 particles can leave via B at a time .
lets say 10 particle enter the pipe per second that means 10 particles must leave the pipe per second, but only 2 particles can leave the pipe at once so to make this possible the pipe will have to eject 2 particles in 0.2 seconds i.e. the particle at A is taking 1 second to cover “x” distance and particle at B is taking 0.2 seconds for the same.
We can thus conclude that speed of particles at B is more than speed of particles at A
the area of cross section at A > area of cross section at B
NOW
Pressure is change of moment felt on the walls of a container due to particles colliding at its walls per unit area (more collisions in a second per unit area more is the pressure felt)
Now refer to figure 2:
There is a wall bouncing between two walls at a constant speed and creates some pressure at point of collisions.
If now one of the wall start to move towards the other then the number of collisions of the ball and the wall per unit time increases and the pressure felt by the walls increases although the speed of the ball has not changed
Now back to figure 1: Same is happening here as the particles move towards B the walls of the pipe gets closer and closer to each other and the particles collide more number of times with the walls per second and an increase in pressure is observed
Hope it helps u
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Answer:
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