渣浆泵液体在叶轮中的运动及能量方程

一、 液体在叶轮中的运动及速度三角形

液体在叶轮中一方面随着叶轮起旋转，作圆周运动，其速度为圆周速度口，与圆周相切。同时液体又从旋转着的时轮从里向外流动，称相对运动，其速度称力相对速度w。液体相对于不动的泵壳的运动是绝对运动，其速度称为绝对速度 v。绝对速度v的向量等于圆周速度u和相对速度w的向量和，即
                             V=u+w  

圆周速度u的方向与叶轮圆周切线方向一致，相对速度w的方向与叶片相切。绝对速度v的方向为圆周速度u和相对速度w的合成，如图2-29所示。相对速度w与圆周速度的夹角β即为叶片安放角。绝对速度V与圆周速度u间的夹角a，称液流角。叶轮中任一液体质点的相对速度、圆周速度及绝对速度三个速度的向量所组成的三角形称为速度三角形。为了作出速度三角形，通常把绝对速度分解成两个相互垂直的分速度:一个是圆周分速度vu;另一个是与圆周速度垂直的分速度，称轴面速度tm。时轮中任一质点都可以作出速度三角形，但以叶片进口和出口的速度三角形最为重要。
1.进口速度三角形
    如图2-30所示，进口速度角形是指液体刚进叶轮叶片进口边时的速度三角形。

进口圆周速度u1：

U1=πD1n/60
式中  u1----叶轮叶片进口边的圆周速度，m/s;

D1----叶轮叶片的进口边直径，m;

n----叶轮转速，r/ min。

进口轴面速度Vmi :

vu1是叶轮叶片进口处绝对速度的圆周分速度，对于叶轮吸入口没有速度环量(即无旋转)，例锥形管吸水室，vu1 ≈0。如采用半螺旋形吸入室等结构，是有速度环量，应根据具体结构求得。
    β1是叶片进口安装角，即为叶片进口与圆周的夹角。
2.出口速度三角形
    如图2 - 31所示，出口速度三角形是指叶轮叶片出口边上但尚未流出出口边时的速度三角形。
进口圆周速度u2:
                       u2=πD2n/60

式中  u2----叶轮叶片出口处的圆周速度， m/s;

D2----叶轮出口直径，m。

出口轴面速度Vm2:

vm2 =Qt/2πR2b2ψ2
式中  Vm----叶轮叶片出口边 上的轴面速度，m/s;
      R2----叶轮出口半径，m;

b2----叶轮出口宽度，m;

u2是叶轮叶片出口处绝对速度的圆周分速度。

β2是叶片出口安装角，即为叶片出口与圆周的夹角。

二、离心泵基本方程式一能 量方程

叶轮传给单位液体的能量叫理论扬程H。反映离心泵理论扬程与液体在叶轮中运动状态关系的方程式称离心泵的基本方程式——能量方程式。从动量矩定律得到:单位时间内流过叶轮的流体的动量矩的改变(增值)应等于作用于该流体的外力矩( 即是叶轮的力矩):

单位时间内叶轮对流体所做的功为Mo,它应等于单位时间内流过叶轮的流体所得到的总能量yHQr,经过运算，即可得到泵的基本方程式:
1.两种特殊情况下的理论扬程
    1)当液体无旋的进入叶轮时，如锥形管吸入室，在设计工况下，叶轮入口绝对速度

的圆周分速度vu1很小，可近似为0,即vu1≈0

Ht=u2vu2/g
(2)为估算泵的扬程，一般情况下vu2≈u2/2；则
                       HT =u2/2g
    利用上式在知道叶轮直径的情况下，可以近似地估算出泵的扬程。

2.有限叶片数的理论扬程

在应用离心泵基本方程式时，为了方便计算，通常假设叶轮里的叶片是无穷多的。出口处相对速度的方向与叶片切线方向完全一致，这时称无限多叶片的理论扬程HT。:
    但实际上叶轮的叶片数是有限的，出口处相对速度的方向并未与叶片切线方向一致，所以有限叶片的理论扬程H比Hr要小，目前还没有精确的计算方法，常用下面经验公式计算 渣浆泵厂家

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