Lecture No. 5
CLASSIFICATION OF FLUID FLOW AND THE CONTINUITY EQUATION
5.1 Classification of Fluid Flow
If the velocity of the fluid is the same in magnitude and direction at every point in the fluid the flow is said to be uniform. Non-uniform flow
A non-uniform flow is one where the velocities at different points at a given instant are not the same. Every fluid that flows near a solid boundary will be non-uniform because the fluid at the boundary takes the velocity of the boundary which is usually zero. Steady flow
A steady flow is one in which the conditions (i.e., velocity, pressure, cross-section) may vary from point to point but do not change with time. Unsteady flow
If at any point in the fluid, the conditions change with time, the flow is unsteady. In reality, there are always slight variations in velocity and pressure; however, if the average values are constant, the flow may be considered steady. Steady uniform flow
In steady uniform flow, conditions do not change with position in the stream or with time.
Example: Flow of water in a pipe of constant diameter at constant velocity
Steady non-uniform flow
In this flow classification, conditions change from point to point in the stream but do not change with time.
Example: Fluid flow in a tapering pipe with constant velocity at the inlet. Velocity will change as the fluid moves along the length of the pipe toward the exit. Unsteady uniform flow
In this flow, the conditions at all points are uniform at any given instant but change with time.
Example: Flow of fluid through a constant-diameter pipe connected to a pump pumping at constant rate which is then switched off. Unsteady non-uniform flow
If every condition of the flow changes from point to point and changes with time at every point, the flow is unsteady and non-uniform.
Example: Waves in a channel
Classification based on restraining effect of solid boundary Closed-conduit flow
Flows which are completely enclosed by restraining solid surface (e.g., flow through pipes and tubes) Open-channel flow
Flows where one surface of the fluid is exposed to the atmosphere (e.g., flow of river, flow of water in irrigation) Free-surface flow
Flow in which the fluid is not in contact with any solid surface (e.g., water jet from a hose, rainfall)
5.2 Incompressible and Compressible Flow
Incompressible fluid flow:
flow in which the fluid’s density is constant;
may be assumed for liquid flow
Compressible fluid flow:
flow in which the fluid’s density changes
true for practically all gases
5.3 Three-dimensional flow
In general, fluid flow is three-dimensional with pressures, velocities and other flow conditions varying in all directions. However, in many cases the most significant changes only occur in two directions or even only in one. One-dimensional flow. Example: flow in a pipe (see Figure 5.1)
Figure 5.1. One-dimensional flow in a pipe
Two-dimensional flow. Example: Flow over a weir for which typical streamlines are seen in Figure 5.2
Figure 5.2. Two-dimensional flow over a weir
5.4 Streamlines and Streamtubes
Streamlines are imaginary curves drawn through a fluid to indicate the direction of motion in various sections of the flow of the fluid system. As such, they are visualization of flow patterns which are drawn by connecting points of equal velocity. Figure 5.3 shows a simple example the streamlines around the cross-section of an aircraft-wing-shaped body.
Figure 5.3. Streamlines around a wing-shaped body
Streamlines that are close to a boundary are parallel to that boundary. At all points the direction of the streamline is the direction of the fluid velocity. In the case of unsteady flow, the position of streamlines can change with time. In steady flow, the position of streamlines does not change. The fluid is moving in the same direction of streamlines; therefore, the fluid cannot cross a...
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