Summary of knowledge points in fluid mechanics

Chapter One Introduction

1 Liquid and gas are collectively referred to as fluid. The basic characteristic of fluid is fluidity. As long as shear stress exists, the flow will continue. Fluid cannot bear shear stress when it is still.

2 Hypothesis of fluid continuum: The fluid is studied as a continuum composed of dense particles and without voids inside.

3 Research methods of fluid mechanics: theory, numerical value, experiment.

4 Forces acting on the fluid

(1) Surface force: The force acting on the surface of the fluid taken through direct contact.

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Chapter 3 Fundamentals of Fluid Dynamics

1 Basic concept:

(1) Fluid particle (particle): a fluid micro-cluster with a small volume, and the fluid is continuously composed of this fluid micro-cluster.

(2) Spatial point: The spatial point is only a geometric point representing the spatial position, not the actual fluid microcluster.

(3) Flow field: a space filled with moving continuous fluid. In the flow field, each fluid particle has certain motion elements.

(4) Local acceleration (time-varying acceleration): at a certain spatial position, the rate of change of the velocity of the fluid particle with time.

Migration acceleration (displacement acceleration): The velocity change rate caused by the change of the spatial position of the fluid particle at an instant.

(5) Steady flow and non-stationary flow: A flow with time as the standard and motion parameters at each space point not changing with time is a constant flow. Otherwise it is a non-steady flow.

(6) Unary flow: The motion parameters are just a function of spatial coordinates and time variables.

Binary flow: Motion parameters are functions of only two spatial coordinates and a time variable.

Ternary flow: Taking space as the standard, the motion parameters at each space point are functions of three space coordinates and time.

(7) Streamline: the curve of the flow direction at a certain moment, and the velocity vectors of each particle on the curve are tangent to the curve.

streamlined nature

(1) The tangent direction of each point on the streamline represents the velocity direction of these points in the flow field at the same time, so the shape of the streamline generally changes with time.

(2) Streamlines generally do not intersect (also intersect in special cases: V=0, speed=

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(3) The streamline does not turn, but is a smooth curve.

(8) Trajectory: the trajectory of fluid particles in a period of time.

Traces and streamlines

(1) In a steady flow, the streamlines are geometrically consistent with the trajectory.

similarities and differences

(2) In unsteady flow, the two generally overlap, but in some cases (V=C) the two can still overlap.

(9) Flow tube: at a certain moment, a closed curve is drawn arbitrarily in the flow field, and streamlines are drawn through each point on the curve to form a tubular surface.

Stream: A flow tube filled with fluid.

(10) Flow cross section: a cross section perpendicular to all streamlines made on the stream. There are flat and curved cross-sections.

(11) Elementary flow: a stream with an infinitely small cross-section, the geometric characteristics of which are the same as streamlines.

Total flow: A stream with a finite cross-section, which is composed of countless element flows, and the motion parameters of each point on the cross-section are different.

(12) Volume flow rate: The flow rate passing through a flow section of the stream per unit time is measured by volume.

Weight flow: The flow rate passing through a flow section of a stream per unit time is measured by weight.

Mass flow rate: The flow rate passing through a flow section of a stream per unit time is measured by mass.

(13) Cross-sectional average flow velocity: the quotient obtained by dividing the volume flow through the effective cross-section by the effective cross-sectional area.

(14) Uniform flow and non-uniform flow: if the streamlines are parallel and straight lines, the flow is uniform flow, otherwise it is non-uniform flow.

properties of uniform flow

1> The migration acceleration of the fluid is zero;

2> Streamlines are parallel straight lines;

3> The flow velocity distribution on each flow section remains unchanged along the way.

4> Dynamic pressure distribution law = static pressure distribution law.

(15) Non-uniform gradual flow and rapid flow: In non-uniform flow, the curvature of the streamline is very small, and the flow of the streamline approximately parallel to the line is non-uniform gradual flow, otherwise it is rapid flow. All properties of uniform flow are applicable to gradually changing flow.

2 Euler method