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動量方程 與渣漿泵動量矩方程

一、 動量方程

一元定常流動的動量定律:單位時間內流出控制面(邊界面) (如圖1 -5中的ABCD)與流入控制面流體的動量之差，等于控制面內流體所受外力之向量和。動量方程為:

作用在流體上的外力包括流體的質量力，固體作用在流體上的力及控制面外的流體作用在控制面邊界處流體的力。
二、動量矩方程
    一元定常流體的動量矩定律:單位時間內流出控制面流體的動量對任一定點0之矩與流入控制面流體的動量對同一定點 0之矩的差，等于控制面中的流體所受外力對于0點之矩的向量和。動量矩方程式為:

      第五節 流動阻 力和能量損失
一、流動阻力分類
    實際流體在流動過程中，因黏滯力的作用，流體之間，流體與固體壁面之間有摩擦力及固壁對流體擾動作用，將會引起能量損失。阻力損失可分為兩類，一類是沿程阻力損失h;另一類是局部阻力損失 h?？偟膿p失應是兩者之和: h. =Zh, + Zh。
1.沿程阻力損失h,
    它是沿流動路程上，由于各流體層之間內摩擦力及流體與固體壁面之間的摩擦力而產生的流動阻力損失。在層流狀態下，沿程阻力完全是由黏性摩擦產生的。在紊流狀態下，沿程阻力一部分是由附面層內的黏性摩擦產生的，另外是由流體微團的遷移和脈動所造成的。
2.局部阻力損失h;
    它是由于流體通過局部障礙時(如閥門、彎頭、管道的突然擴大或縮小等)，干擾了液

體的運動，改變了速度分布、產生漩渦、沖擊等所產生的阻力損失h。
二、沿程阻力損失hn,的計算

1. 沿程阻力損失計算公式

hf=λ·L/d·v2/2g

式中hf-----沿程阻力損失，m;

L------管道長度，m;

d------管道直徑，m;

v------平均流速， m/s;

g-----重力加速度，m/s;

λ-----沿程阻力系數， 無量綱的量，與流動狀態有關。

計算時應注意，管道直徑不同時，應分段計算后相加為總的沿程阻力損失h。

2. 流動狀態與雷諾數

在上面提到過沿程阻力由于流動狀態不同,阻力是不同的,在層流狀態下，沿程阻力完全是由黏性摩擦產生的;在紊流狀態下，一部分由附面層內黏性摩擦產生，另外是由流體微團的遷移和脈動造成的，那么什么是層流，什么是紊流呢?
    1)層流:當管內流動速度小于某一確定值時，液體作有規則的層狀或流束狀運動，各層互不干擾，互不相混，流線平行，這種狀態稱為層流運動。
    2)紊流:當管內流動速度大于某一確定值 vkp時，液體質點不再作規則的層狀運動。而是交錯混亂地向前運動，液體質點除縱向運動外，還附加有橫向運動，這種運動稱為紊流，實際使用中，一般為紊流運動。 層流和紊流的判別式為雷諾數Re。
    3)雷諾數Re
                          Re =vd/v
式中  v---平均流速，m/s;
      d---管道直徑，m;
      v---運動黏性系數，m2/s;

Re---雷諾數，無量綱;

當Re≤2320時，層流;

Re >2320時，紊流。

在工程計算中，常以Re =2000為臨界雷諾數,

即Re <2000時，層流;

Re>2000時，紊流。
3.沿程阻力系數λ的計算
    沿程阻力系數λ與流動狀態雷諾數有關，并和管道的表面相對粗糙度有關，即:
λ=f (Re, R,/D)

當Re <2000時
λ=64/Re

當Re>2000時，各紊流狀態λ值與雷諾數Re有關，并且還與管道的相對粗糙度有關。計算相當困難，各國學者推薦了很多經驗公式，這里介紹一種比較簡單的查圖方法。用圖1- 6莫迪圖來查出沿程阻力系數λ。圖中Ra/D為相對粗糙度，Ra為管道壁表面的粗糙度，D為管道的直徑。表1 -4表示了各種材料管道壁的表面粗糙度R。。

對于我們常用的無銹蝕的鋼管在輸送水的情況下，可查圖1-7沿程阻力系數λ值更為方便。渣漿泵

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