（免费）报完志愿必看！第二堂暑假必修课！快快转给家庭群让孩子们学起来《流体稳定性湍流》例题解析【Unity·Unità VII】

1.Suction applied on fully developed laminar boundary layer flow over a flat plate ASBL, compute u,v,w and p

Answer:

Couette Flow, a basic concept in fluid dynamics, examines the flow of viscous fluids constrained between two surfaces. One surface is typically at rest while the other is moving tangentially, driving the fluid flow. The primary force at play here is the viscous resistance to shear stress. It's noteworthy because it's used to study shear flow and viscosity characteristics in many engineering and scientific applications.

Couette Flow 是流体动力学的一个基本概念，它检查了约束在两个表面之间的粘性流体的流动。一个表面通常处于静止状态，而另一个表面切向移动，驱动流体流动。这里起作用的主要力量是对剪切应力的粘性抵抗力。值得一提的是，它用于研究许多工程和科学应用中的剪切流和粘度特性。

In fluid mechanics, "fully developed flow" refers to a flow condition in which the velocity profile across a cross-section of a pipe or channel remains constant along the flow direction. This typically occurs after a certain distance downstream from the entrance of the pipe or channel, where the flow has had sufficient distance to adjust and stabilize.

在流体力学中，“完全展开的流动”是指管道或通道横截面上的速度曲线沿流动方向保持恒定的流动条件。这通常发生在管道或通道入口下游一定距离后，那里的流量有足够的距离来调节和稳定。

Physically, fully developed flow means that the flow pattern has reached a steady state and the velocity profile no longer changes with respect to the flow direction. In other words, the flow has settled into a consistent pattern where the velocity distribution across the cross-section remains the same at any given point along the length of the pipe or channel.

从物理上讲，完全发展的流动意味着流动模式已达到稳定状态，并且速度曲线不再相对于流动方向发生变化。换言之，流动已经形成一致的模式，即在管道或通道长度的任何给定点上，横截面上的速度分布保持不变。

A flow is called fully developed flow when the velocity profile does not change with streamwise direction. Physically, there would be no change in velocity profile as you march towards streamwise direction. Mathematically:

当速度剖面不随流向变化时，流称为完全展开流。从物理上讲，当您向流向方向前进时，速度曲线不会发生变化。数学表达：

δu/δx=0

For example, in a pipe, fully developed flow implies that the velocity profile is parabolic, with the maximum velocity occurring at the center of the pipe and decreasing towards the walls. This is a characteristic of laminar flow in a pipe, known as the Poiseuille flow profile.

例如，在管道中，完全展开的流动意味着速度剖面是抛物线的，最大速度发生在管道的中心，并朝向壁递减。这是管道中层流的特征，称为泊塞耶流剖面。

对于Couette flow，

由此我们可以得到 u = Ay+B, v = 0, w = 0, p = p(x).

对于Couette flow, p = p0，因为其不具备pressure gradient.

下题预告：

2)Function relation of u(y); Navier-Stokes equations;

3)incompressible, inviscous, irrotational flow, vortex stretch; 2D flow;

4)Poiseuille flow, average (bulk) velocity; total wall friction force channel and pipe flow; u central-line, profile of flow.

... ...

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