动量方程 与渣浆泵动量矩方程

一、 动量方程

一元定常流动的动量定律:单位时间内流出控制面(边界面) (如图1 -5中的ABCD)与流入控制面流体的动量之差，等于控制面内流体所受外力之向量和。动量方程为:

作用在流体上的外力包括流体的质量力，固体作用在流体上的力及控制面外的流体作用在控制面边界处流体的力。
二、动量矩方程
    一元定常流体的动量矩定律:单位时间内流出控制面流体的动量对任一定点0之矩与流入控制面流体的动量对同一定点 0之矩的差，等于控制面中的流体所受外力对于0点之矩的向量和。动量矩方程式为:

      第五节 流动阻 力和能量损失
一、流动阻力分类
    实际流体在流动过程中，因黏滞力的作用，流体之间，流体与固体壁面之间有摩擦力及固壁对流体扰动作用，将会引起能量损失。阻力损失可分为两类，一类是沿程阻力损失h;另一类是局部阻力损失 h。总的损失应是两者之和: h. =Zh, + Zh。
1.沿程阻力损失h,
    它是沿流动路程上，由于各流体层之间内摩擦力及流体与固体壁面之间的摩擦力而产生的流动阻力损失。在层流状态下，沿程阻力完全是由黏性摩擦产生的。在紊流状态下，沿程阻力一部分是由附面层内的黏性摩擦产生的，另外是由流体微团的迁移和脉动所造成的。
2.局部阻力损失h;
    它是由于流体通过局部障碍时(如阀门、弯头、管道的突然扩大或缩小等)，干扰了液

体的运动，改变了速度分布、产生漩涡、冲击等所产生的阻力损失h。
二、沿程阻力损失hn,的计算

1. 沿程阻力损失计算公式

hf=λ·L/d·v2/2g

式中hf-----沿程阻力损失，m;

L------管道长度，m;

d------管道直径，m;

v------平均流速， m/s;

g-----重力加速度，m/s;

λ-----沿程阻力系数， 无量纲的量，与流动状态有关。

计算时应注意，管道直径不同时，应分段计算后相加为总的沿程阻力损失h。

2. 流动状态与雷诺数

在上面提到过沿程阻力由于流动状态不同,阻力是不同的,在层流状态下，沿程阻力完全是由黏性摩擦产生的;在紊流状态下，一部分由附面层内黏性摩擦产生，另外是由流体微团的迁移和脉动造成的，那么什么是层流，什么是紊流呢?
    1)层流:当管内流动速度小于某一确定值时，液体作有规则的层状或流束状运动，各层互不干扰，互不相混，流线平行，这种状态称为层流运动。
    2)紊流:当管内流动速度大于某一确定值 vkp时，液体质点不再作规则的层状运动。而是交错混乱地向前运动，液体质点除纵向运动外，还附加有横向运动，这种运动称为紊流，实际使用中，一般为紊流运动。 层流和紊流的判别式为雷诺数Re。
    3)雷诺数Re
                          Re =vd/v
式中  v---平均流速，m/s;
      d---管道直径，m;
      v---运动黏性系数，m2/s;

Re---雷诺数，无量纲;

当Re≤2320时，层流;

Re >2320时，紊流。

在工程计算中，常以Re =2000为临界雷诺数,

即Re <2000时，层流;

Re>2000时，紊流。
3.沿程阻力系数λ的计算
    沿程阻力系数λ与流动状态雷诺数有关，并和管道的表面相对粗糙度有关，即:
λ=f (Re, R,/D)

当Re <2000时
λ=64/Re

当Re>2000时，各紊流状态λ值与雷诺数Re有关，并且还与管道的相对粗糙度有关。计算相当困难，各国学者推荐了很多经验公式，这里介绍一种比较简单的查图方法。用图1- 6莫迪图来查出沿程阻力系数λ。图中Ra/D为相对粗糙度，Ra为管道壁表面的粗糙度，D为管道的直径。表1 -4表示了各种材料管道壁的表面粗糙度R。。

对于我们常用的无锈蚀的钢管在输送水的情况下，可查图1-7沿程阻力系数λ值更为方便。渣浆泵

Momentum equation and momentum moment equation

Momentum equation

The momentum law of one-dimensional steady flow: the difference between the momentum of the fluid flowing out of the control surface (edge interface) (as shown in Figure 1-5) and flowing in the control surface in unit time is equal to the vector sum of the external forces on the fluid in the control surface. The momentum equation is:

The external force acting on the fluid includes the mass force of the fluid, the force of the solid acting on the fluid and the force of the fluid acting on the boundary of the control surface.

Moment of momentum equation

The law of momentum moment of one-dimensional steady fluid: the difference between the moment of momentum of the fluid flowing out of the control surface at any point 0 and the moment of momentum of the fluid flowing into the control surface at the same point 0 in unit time is equal to the vector sum of the external force on the fluid in the control surface at 0 point. The momentum moment equation is:

Section 5 flow resistance and energy loss

I. classification of flow resistance

In the actual process of fluid flow, due to the effect of viscous force, there is friction between fluids, between fluids and solid walls, and solid walls disturb the fluid, which will cause energy loss. The resistance loss can be divided into two categories, one is the resistance loss h along the way, the other is the local resistance loss H. The total loss should be the sum of the two: h. = Zh, + zh.

1. Resistance loss along the way h,

It is the loss of flow resistance along the flow path due to the internal friction between the fluid layers and the friction between the fluid and the solid wall. In laminar flow, the frictional resistance is completely caused by viscous friction. In turbulent flow, part of the drag is caused by the viscous friction in the boundary layer, and the other is caused by the migration and pulsation of the fluid micro cluster.

2. Local resistance loss h;

It interferes with the liquid when the fluid passes through local obstacles (such as sudden expansion or reduction of valves, elbows, pipes, etc.)

The movement of the body changes the resistance loss h caused by velocity distribution, vortex and impact.

2. Calculation of resistance loss HN, along the way

1. Calculation formula of resistance loss along the way

hf=λ·L/d·v2/2g

Where HF is the resistance loss along the way, m;

L ------ pipe length, m;

D -- pipe diameter, m;

V ------ average velocity, M / S;

G -- acceleration of gravity, M / S;

λ - drag coefficient along the path, dimensionless quantity, related to the flow state.

When calculating, it should be noted that when the pipe diameter is different, it should be added up to the total resistance loss h along the way after section calculation.

2. Flow state and Reynolds number

As mentioned above, due to different flow states, the resistance is different. In the laminar flow state, the resistance is completely generated by viscous friction; in the turbulent flow state, part of the resistance is generated by viscous friction in the boundary layer, in addition, it is caused by the migration and pulsation of fluid micro clusters, so what is laminar flow and what is turbulent flow?

1) laminar flow: when the flow velocity in the pipe is less than a certain value, the liquid moves in a regular layer or flow beam shape, each layer does not interfere with each other, do not mix with each other, and the streamline is parallel. This state is called laminar flow movement.

2) turbulent flow: when the flow velocity in the pipe is greater than a certain value VKP, the liquid particle will not make regular layered motion. It moves forward in a staggered and disordered way. In addition to the longitudinal motion, the liquid particle also has a lateral motion, which is called turbulence. In practice, it is generally turbulence The discriminant of laminar and turbulent flow is Reynolds number Re.

3) Reynolds number Re

Re =vd/v

Where V is the average velocity, M / S;

D -- pipe diameter, m;

V -- kinematic viscosity coefficient, m2 / S;

Re - Reynolds number, dimensionless;

When re ≤ 2320, laminar flow;

When re > 2320, turbulence.

In engineering calculation, the critical Reynolds number is re = 2000,

When Re < 2000, laminar flow;

When re > 2000, turbulence.

3. Calculation of resistance coefficient λ

The drag coefficient λ is related to the Reynolds number of the flow state and the relative roughness of the pipe surface, namely:

λ=f (Re, R,/D)

When Re < 2000

Lambda =64/Re

When re > 2000, the λ value of each turbulent state is related to the Reynolds number Re, and also to the relative roughness of the pipeline. It's very difficult to calculate. Scholars from all over the world have recommended many empirical formulas. Here, we introduce a relatively simple method of mapping. The resistance coefficient λ along the path is found out by using the modi diagram in Figure 1-6. In the figure, RA / D is the relative roughness, RA is the roughness of the pipe wall surface, and D is the diameter of the pipe. Table 1-4 shows the surface roughness r of pipe wall of various materials..

It is more convenient to check the value of resistance coefficient λ in Figure 1-7 for the commonly used steel pipes without corrosion when transporting water. Slurry pump