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渣漿泵液體在葉輪中的運動及能量方程

一、 液體在葉輪中的運動及速度三角形

液體在葉輪中一方面隨著葉輪起旋轉，作圓周運動，其速度為圓周速度口，與圓周相切。同時液體又從旋轉著的時輪從里向外流動，稱相對運動，其速度稱力相對速度w。液體相對于不動的泵殼的運動是絕對運動，其速度稱為絕對速度 v。絕對速度v的向量等于圓周速度u和相對速度w的向量和，即
                             V=u+w  

圓周速度u的方向與葉輪圓周切線方向一致，相對速度w的方向與葉片相切。絕對速度v的方向為圓周速度u和相對速度w的合成，如圖2-29所示。相對速度w與圓周速度的夾角β即為葉片安放角。絕對速度V與圓周速度u間的夾角a，稱液流角。葉輪中任一液體質點的相對速度、圓周速度及絕對速度三個速度的向量所組成的三角形稱為速度三角形。為了作出速度三角形，通常把絕對速度分解成兩個相互垂直的分速度:一個是圓周分速度vu;另一個是與圓周速度垂直的分速度，稱軸面速度tm。時輪中任一質點都可以作出速度三角形，但以葉片進口和出口的速度三角形最為重要。
1.進口速度三角形
    如圖2-30所示，進口速度角形是指液體剛進葉輪葉片進口邊時的速度三角形。

進口圓周速度u1：

U1=πD1n/60
式中  u1----葉輪葉片進口邊的圓周速度，m/s;

D1----葉輪葉片的進口邊直徑，m;

n----葉輪轉速，r/ min。

進口軸面速度Vmi :

vu1是葉輪葉片進口處絕對速度的圓周分速度，對于葉輪吸入口沒有速度環量(即無旋轉)，例錐形管吸水室，vu1 ≈0。如采用半螺旋形吸入室等結構，是有速度環量，應根據具體結構求得。
    β1是葉片進口安裝角，即為葉片進口與圓周的夾角。
2.出口速度三角形
    如圖2 - 31所示，出口速度三角形是指葉輪葉片出口邊上但尚未流出出口邊時的速度三角形。
進口圓周速度u2:
                       u2=πD2n/60

式中  u2----葉輪葉片出口處的圓周速度， m/s;

D2----葉輪出口直徑，m。

出口軸面速度Vm2:

vm2 =Qt/2πR2b2ψ2
式中  Vm----葉輪葉片出口邊 上的軸面速度，m/s;
      R2----葉輪出口半徑，m;

b2----葉輪出口寬度，m;

u2是葉輪葉片出口處絕對速度的圓周分速度。

β2是葉片出口安裝角，即為葉片出口與圓周的夾角。

二、離心泵基本方程式一能 量方程

葉輪傳給單位液體的能量叫理論揚程H。反映離心泵理論揚程與液體在葉輪中運動狀態關系的方程式稱離心泵的基本方程式——能量方程式。從動量矩定律得到:單位時間內流過葉輪的流體的動量矩的改變(增值)應等于作用于該流體的外力矩( 即是葉輪的力矩):

單位時間內葉輪對流體所做的功為Mo,它應等于單位時間內流過葉輪的流體所得到的總能量yHQr,經過運算，即可得到泵的基本方程式:
1.兩種特殊情況下的理論揚程
    1)當液體無旋的進入葉輪時，如錐形管吸入室，在設計工況下，葉輪入口絕對速度

的圓周分速度vu1很小，可近似為0,即vu1≈0

Ht=u2vu2/g
(2)為估算泵的揚程，一般情況下vu2≈u2/2；則
                       HT =u2/2g
    利用上式在知道葉輪直徑的情況下，可以近似地估算出泵的揚程。

2.有限葉片數的理論揚程

在應用離心泵基本方程式時，為了方便計算，通常假設葉輪里的葉片是無窮多的。出口處相對速度的方向與葉片切線方向完全一致，這時稱無限多葉片的理論揚程HT。:
    但實際上葉輪的葉片數是有限的，出口處相對速度的方向并未與葉片切線方向一致，所以有限葉片的理論揚程H比Hr要小，目前還沒有精確的計算方法，常用下面經驗公式計算 渣漿泵廠家

Motion and energy equation of slurry pump liquid in impeller

I. movement and velocity triangle of liquid in impeller

On the one hand, the liquid in the impeller rotates with the impeller and moves in a circular motion. Its speed is a circular velocity port, tangent to the circumference. At the same time, the liquid flows out of the rotating wheel, which is called relative motion, and its velocity is called relative velocity of force W. The motion of the liquid relative to the stationary pump shell is absolute, and its velocity is called absolute velocity v. The vector of absolute velocity V is equal to the sum of the vectors of the peripheral velocity u and the relative velocity W, i.e

V=u+w

The direction of the circumferential velocity u is the same as the tangential direction of the impeller circumference, and the direction of the relative velocity W is tangent to the blade. The direction of absolute velocity V is the combination of circumferential velocity u and relative velocity W, as shown in Figure 2-29. The angle β between the relative velocity W and the peripheral velocity is the blade angle. The angle a between the absolute velocity V and the peripheral velocity u is called the liquid flow angle. The triangle formed by the vector of relative velocity, circumferential velocity and absolute velocity of any liquid particle in the impeller is called velocity triangle. In order to make velocity triangles, the absolute velocity is usually divided into two sub velocities which are perpendicular to each other: one is the peripheral sub velocity Vu; the other is the sub velocity which is perpendicular to the peripheral velocity, which is called axial velocity TM. The velocity triangles can be made for any particle in the wheel, but the velocity triangles at the inlet and outlet of the blade are the most important.

1. Inlet speed triangle

As shown in Figure 2-30, the inlet velocity angle refers to the velocity triangle when the liquid just enters the inlet side of the impeller blade.

Inlet circumferential speed U1:

U1= PI D1n/60

Where, U1 is the circumferential velocity of the inlet edge of impeller blade, M / S;

D1 -- diameter of inlet side of impeller blade, m;

N ---- impeller speed, R / min.

Inlet axial speed VMI:

Vu1 is the peripheral velocity of the absolute velocity at the impeller blade inlet. There is no velocity circulation (i.e. no rotation) at the impeller inlet. For example, the conical pipe suction chamber, vu1 ≈ 0. If half spiral suction chamber is adopted, it has velocity circulation, which should be calculated according to the specific structure.

β 1 is the installation angle of the blade inlet, that is, the angle between the blade inlet and the circumference.

2. Outlet speed triangle

As shown in Figure 2-31, the outlet velocity triangle refers to the velocity triangle on the outlet edge of the impeller blade but not yet flowing out of the outlet edge.

Inlet circumferential speed U2:

U2= PI D2n/60

Where U2 is the peripheral velocity at the outlet of impeller blade, M / S;

D2 ---- impeller outlet diameter, M.

Outlet axial speed vm2:

vm2 =Qt/2πR2b2ψ2

Where VM is the axial speed on the outlet edge of impeller blade, M / S;

R2 ---- impeller outlet radius, m;

B2 ---- impeller outlet width, m;

U2 is the peripheral velocity of the absolute velocity at the impeller blade outlet.

β 2 is the installation angle of the blade outlet, that is, the angle between the blade outlet and the circumference.

Basic equation of centrifugal pump energy equation

The energy transmitted by impeller to unit liquid is called theoretical lift H. The equation that reflects the relationship between the theoretical head of centrifugal pump and the motion state of liquid in impeller is called the basic equation of centrifugal pump energy equation. According to the law of moment of momentum, the change (increment) of the moment of momentum of the fluid flowing through the impeller in unit time should be equal to the external moment acting on the fluid (that is, the moment of the impeller):

The work done by the impeller to the fluid in unit time is mo, which should be equal to the total energy yhqr obtained by the fluid flowing through the impeller in unit time. After calculation, the basic equation of the pump can be obtained:

1. Theoretical lift in two special cases

1) when the liquid enters the impeller without rotation, such as the conical pipe suction chamber, under the design condition, the absolute speed of the impeller inlet

The circumferential velocity of vu1 is very small, which can be approximated to 0, that is, vu1 ≈ 0

Ht=u2vu2/g

(2) in order to estimate the head of the pump, in general, vu2 ≈ U2 / 2; then

HT =u2/2g

Using the above formula, the pump head can be estimated approximately when the impeller diameter is known.

2. Theoretical lift of finite number of blades

In the application of the basic equations of centrifugal pump, in order to facilitate the calculation, it is usually assumed that there are infinite blades in the impeller. The direction of the relative velocity at the exit is exactly the same as the tangent direction of the blade, which is called the theoretical lift ht of infinite blades. :

But in fact, the number of blades of impeller is limited, and the direction of relative velocity at the outlet is not consistent with the tangent direction of blade, so the theoretical lift h of finite blade is smaller than HR, and there is no accurate calculation method at present. The following empirical formula is commonly used to calculate the slurry pump manufacturer