流体力学上课讲义第四章-1

流体力学上课讲义第四章-1

4 Flowing Fluids and Pressure Variation

Engineering Fluid Mechanics9th Edition SI Version

流体力学上课讲义第四章-1

流体力学上课讲义第四章-1

4.1 Description of Fluid Motion To visualize the flow field, it’s desirable to construct lines that show flow direction; the collection of the lines is called flow pattern. Streamline: a curve that is everywhere tangent to the local velocity vector at that instant. Pathline: the actual path traveled by an individual fluid particle over some time period. Streakline: the line generated by a tracer fluid continuously injected into the flow field at the starting point.

FIGURE 4–12 Cimbala& Cengel Spinning baseball. Flow field visualized using smoke.

流体力学上课讲义第四章-1

Streamline Streamline: a curve that is everywhere tangent to the local velocity vector at that instant. The tangent of the streamline at a given point gives the direction of the velocity vector. The streamline, however, does not indicate the magnitude of the velocity.

Figure. 4.1 Flow through an opening in a tank and over an airfoil section

流体力学上课讲义第四章-1

Streamline Streamline cannot be directly observed experimentally except in steady flow fields, in which they are coincident with pathlines and streaklines

Figure 4.2 Predicted streamline pattern over the Volvo ECC prototype.

流体力学上课讲义第四章-1

PathlineThe actual path traveled by an individual fluid particle over some time period.

FIGURE 4–15 Cimbala& Cengel A pathline is formed by following the actual path of a fluid particle

FIGURE 4–16 Cimbala& Cengel Pathlines produced by white tracer particles suspended in water and captured by time-exposure photography; as waves pass horizontally, each particle moves in an elliptical path during one wave period.

流体力学上课讲义第四章-1

StreaklineThe line generated by a tracer fluid continuously injected into the flow field.

FIGURE 4–17 Cimbala& Cengel A streakline is formed by continuous introduction of dye or smoke from a point in the flow. Labeled tracer particles (1 through 8) were introduced sequentially.

FIGURE 4–18 Cimbala& Cengel Streaklines produced by colored fluid introduced upstream; since the flow is steady, these streaklines are the same as streamlines and pathlines.

流体力学上课讲义第四章-1

Uniform vs. Nonuniform flowVelocity of the fluidUniform flow: the velocity does not change along the a fluid path

Nonuniform flow: the velocity changes along the a fluid path

Figure 4.3 Fluid particle moving along a pathline.

Figure 4.4 Uniform flow in a pipe.

流体力学上课讲义第四章-1

Nonuniform flow

Figure 4.5 Flow patterns for nonuniform flow. (a) Converging flow. (b) Vortex flow.

流体力学上课讲义第四章-1

Steady vs. Unsteady flowSteady flow: the velocity at a given point does not change with time Unsteady flow: the velocity at a given point changes with time

V 0 t V 0 tFor example, the flow rate changes due to a valve closing or opening

流体力学上课讲义第四章-1

Streamline: a curve that is everywhere tangent to the instantaneous local velocity vector. Pathline: the actual path traveled by an individual fluid particle over some time period. Streakline: the locus of

fluid particles that have passed sequentially through a prescribed point in the flow.

When the flow is steady, streamlines, pathlines, and streaklines are identical.

流体力学上课讲义第四章-1

Figure 4.6 Streamlines, pathlines, and streakline for an unsteady flow field. Both the pathline and streakline provide a history of the flow field, and the streamlines indicate the current flow pattern.

流体力学上课讲义第四章-1

Laminar vs. Turbulent flow

Laminar flow: well-ordered state of flow in which adjacent fluid layers move smoothly with respect to each other

Turbulent flow: an unsteady flow characterized by intense cross-stream mixing.

流体力学上课讲义第四章-1

Laminar vs. Turbulent flowLaminar flow Turbulent flow

Since turbulent flow is unsteady, the velocity at any point fluctuates with time. The standard approach to treating turbulent flow is to represent the velocity as a time-averaged value plus a fluctuating quantity, A turbulent flow is often designated as“steady” if change with time.

u u u

u does not

流体力学上课讲义第四章-1

One-dimensional and multi-dimensional flowsThe dimensionality of a flow field is characterized by the number of spatial dimensions needed to describe the velocity field. One-dimension

Two-dimension

Three-dimension

流体力学上课讲义第四章-1

4.3 Euler’s Equation

Consider a fluid element oriented and accelerating in an arbitrary l direction. Assume that the viscous forces are zero. Applying Newton’s second law in the l direction

Mass of element

Any pressure acting on the side of the cylindrical element will not contribute to a force in the l direction.

流体力学上课讲义第四章-1

W A lForce due to pressure in the l direction Force due to gravity in the l direction z z Fgravity W A l l l

流体力学上课讲义第四章-1

Substituting the mass and the forces on the element into Eq. (4.6) yields

Dividing through by A l

Taking the limit l 0

For incompressible flow

Euler’s equation

流体力学上课讲义第四章-1

Euler’s Equation ( p z ) al l(4.8)

Euler’s equation shows that Acceleration is equal to the change in piezometric pressure with distance The minus sign means that the acceleration is in the direction of decreasing piezometric pressure In a static fluid, Euler’s equation reduces to ( p z ) 0 lThe hydrostatic differential equation

Euler’s equation can be used to find the pressure required to accelerate a column of fluid.

流体力学上课讲义第四章-1

Assumptions: 1. Acceleration is constant 2. Viscous effects are unimportant 3. Water is incompressible

( p z ) al l

流体力学上课讲义第四章-1

P2=0

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