The flow of the fluid is said to be steady if at any given point, the velocity of each passing fluid particle remains constant in time. This does not mean that the velocity at different points in space is same. The velocity of a particular particle may change as it moves from one point to another.
That is, at some other point the particle may have a different velocity, but every other particle which passes the second point behaves exactly as the previous particle that has just passed that point. Each particle follows a smooth path, and the paths of the particles do not cross each other.
The path taken by a fluid particle under a steady flow is a streamline. It is defined as a curve whose tangent at any point is in the direction of the fluid velocity at that point.
Let us consider the path of a particle as shown in figure below, the curve describes how a fluid particle moves with time. The curve PQ is like a permanent map of fluid flow, indicating how the fluid streams.
No two streamlines can cross, for if they do, an oncoming fluid particle can go either one way or the other and the flow would not be steady. Hence, in steady flow, the map of flow is stationary in time. If we intend to show streamline of every flowing particle, we would end up with a continuum of lines. Consider planes perpendicular to the direction of fluid flow e.g., at three points P, R and Q in figure b.
The plane pieces are so chosen that their boundaries be determined by the same set of streamlines.
In general Av = constant Av gives the volume flux or flow rate and remains constant throughout the pipe of flow. This is called the equation of continuity and it is a statement of conservation of mass in flow of incompressible fluids.
Thus, at narrower portions where the streamlines are closely spaced, velocity increases and its vice versa. From Fig b it is clear that AR > AQ or vR < vQ, the fluid is accelerated while passing from R to Q. This is associated with a change in pressure in fluid flow in horizontal pipes.
Hydrostatics topics :
What is pressure ?
Pressure variation with depth
Pascal's Law
Bulk Modulus
Shear modulus
Elastic behavior of Solids
That is, at some other point the particle may have a different velocity, but every other particle which passes the second point behaves exactly as the previous particle that has just passed that point. Each particle follows a smooth path, and the paths of the particles do not cross each other.
The path taken by a fluid particle under a steady flow is a streamline. It is defined as a curve whose tangent at any point is in the direction of the fluid velocity at that point.
Let us consider the path of a particle as shown in figure below, the curve describes how a fluid particle moves with time. The curve PQ is like a permanent map of fluid flow, indicating how the fluid streams.
No two streamlines can cross, for if they do, an oncoming fluid particle can go either one way or the other and the flow would not be steady. Hence, in steady flow, the map of flow is stationary in time. If we intend to show streamline of every flowing particle, we would end up with a continuum of lines. Consider planes perpendicular to the direction of fluid flow e.g., at three points P, R and Q in figure b.
The plane pieces are so chosen that their boundaries be determined by the same set of streamlines.
In general Av = constant Av gives the volume flux or flow rate and remains constant throughout the pipe of flow. This is called the equation of continuity and it is a statement of conservation of mass in flow of incompressible fluids.Thus, at narrower portions where the streamlines are closely spaced, velocity increases and its vice versa. From Fig b it is clear that AR > AQ or vR < vQ, the fluid is accelerated while passing from R to Q. This is associated with a change in pressure in fluid flow in horizontal pipes.
Hydrostatics topics :
Problems on Bernoulli's theorem and Its Applications
Pressure variation with depth
Pascal's Law
Bulk Modulus
Shear modulus
Elastic behavior of Solids
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