High Head And High Pressure Solution

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1. Definition of Head

Head:The increase in energy per unit mass of liquid transported by a pump from the inlet to the outlet, expressed as the algebraic difference between the total outlet head H2 and the total inlet head H1. Complies with H, in meters. 
Theoretical head: The energy given by the impeller to a unit weight of liquid, usually referring to the theoretical value without considering losses inside the pump.
Rated head:The head that a pump can achieve when conveying a medium at rated flow rate and rated speed.
Maximum head: The head at which the pump flow rate is zero.

In daily life, we can also experiment by placing our hands into a bucket and quickly selecting, causing the water to rotate along with our hands.

Under the action of centrifugal force, the larger the radius of the liquid, the greater the circumferential velocity, the greater the centrifugal force, and the higher the pressure. The liquid level in the bucket is high at the periphery and low at the center, forming a parabolic shape. In fact, the principle of centrifugal pump operation is the same. When the pump is filled with water, the impeller rotates at high speed under the drive of the motor, which drives the rotation of the liquid and increases the energy of the liquid (including kinetic energy and pressure energy) to produce a head.

2. Operating Principle of Centrifugal Pumps

Centrifugal pump is a type of fluid machinery, characterized by obtaining pressure under the influence of continuous flow process. The impeller equipped with blades in the radial structure transfers mechanical energy to the liquid in the impeller channel, and discharges the liquid out of the impeller through centrifugal force. Once the liquid leaves the channel, energy transfer ends. Energy transfer causes an increase in pressure and velocity of the conveying medium.

Under the action of centrifugal force, the pressure in the impeller increases. During the flow of the conveying medium, the relative velocity continuously decreases while the circumferential velocity increases. This is an inevitable phenomenon of increased centrifugal force. After energy transfer is completed at the outlet of the impeller, higher speeds will result in greater hydraulic friction losses. Therefore, the remaining velocity energy must be further converted into pressure energy. In a fixed installation pump system, there is a gradually expanding flow channel that surrounds the outer circumference of the impeller in a ring shape, and the guide vanes can achieve this ability conversion.

The bladeless annular chamber and pressurized water chamber are equally suitable for converting velocity energy into pressure energy (acting as guide vanes).

In a multi-stage pump, the impeller and guide vanes together can form one stage of the pump.

Due to the low-pressure zone generated at the inlet of the pump by the impeller pressure liquid, a pressure difference is formed with the outside to generate suction force. The same volume of liquid enters the pump suction chamber through the suction pipe, thus maintaining continuous medium flow during the rotation of the impeller.

The pressurized water chamber refers to the hydraulic component of the flow passage from the impeller to the pump outlet flange, which is an important part of the pump and an indispensable component of any vane pump.

The pressurized water chamber must complete the following tasks with minimal hydraulic losses: to form stable relative motion conditions inside the impeller, it is necessary to ensure that the flow rate of the liquid in the pressurized water chamber is axisymmetric. The high-speed liquid flowing out of the impeller should be collected, and most of the liquid's kinetic energy should be converted into pressure energy, and then transported to the outlet pressurized water pipeline or to the inlet of the next stage impeller. During the energy conversion process, the axisymmetric flow of the liquid in the pressurized water chamber should not be destroyed. The liquid flowing out of the impeller has a large velocity circulation, while the liquid entering the inlet of the secondary impeller requires its velocity circulation to be basically zero. Therefore, the third function is to eliminate velocity circulation.

The spiral pressurized water chamber consists of spiral flow channels 0-8 with gradually increasing cross-sections and diffusion tubes. Spiral type pressurized water chamber is the most widely used type of centrifugal pump, also known as snail shell or snail body, used in single-stage single suction centrifugal pumps, single suction double suction centrifugal pumps, and horizontal open multi-stage centrifugal pumps.

The flow of liquid in the pressurized water chamber is inertial free flow, which ensures that the liquid flow flowing out of the impeller is not affected by any external force.3. Energy Conversion Process

According to the dynamic moment theorem, it can be inferred that in a spiral flow channel, liquid flows at an equal velocity moment, and the value of the velocity moment is equal to the product of the velocity at the impeller outlet and the impeller outlet radius. As the radius increases, the surrounding velocity decreases. Therefore, a small portion of kinetic energy has already been converted into pressure energy in the spiral section, but this is not sufficient. In the diffusion tube, the velocity of the liquid gradually decreases and the pressure gradually increases, converting kinetic energy into pressure energy and completing the energy conversion task of head.

3. Energy Conversion Process

Basic calculation formula (Bernoulli equation method)
Theoretical lift formula

Among them:
P outlet, P inlet: pump outlet and inlet pressure (Pa or bar x10 ⁵)
ρ: Liquid density (kg/m ³, water ≈ 1000)
g: Gravity acceleration (9.81 m/s ²);
V export v import: export and import flow velocities (m/s);
Z export Z import: height difference between export and import (m).
If the inlet and outlet pipe diameters are the same (V outlet=V outlet), the kinetic energy term can be ignored.

If the height difference can be ignored (such as horizontal installation)

If the inlet pressure is atmospheric pressure (P=0)

Example：
Calculate the head of the water pump
Import pressure p1=0.2 bar (vacuum gauge reading, i.e. -0.2 bar=-20000 Pa)
Export pressure p2=3bar (=300000Pa)
Import and export height difference z2 − z1=0.5m
The inlet and outlet pipe diameters are the same (v1=v2)
Transporting liquid as water (ρ=1000 kg/m ³)

Example 2:   
Estimating head using only outlet pressure
Export pressure gauge reading p2=2.5 bar (=250000 Pa)
Imported at atmospheric pressure (p1=0)
Ignore height and speed differences (z2-z1 ≈ 0, v2 ≈ v1)

By calculating power and flow rate
If the effective power (Pe) and flow rate (Q) of the pump are known, the head can be calculated as

P: Effective power (W), usually the motor power x pump efficiency
η: =Total efficiency of water pump (provided by the manufacturer)
Q: =Flow rate (m/s)=Q (m3/h ÷ 3600)
102 is a constant (derived from 1000 ÷ 9.8=102)
Example 3：
Motor power P=15KW
Flow rate Q=50m3/h=50 ÷ 3600=0.0138m3/s
Total efficiency 65%
H=15X0.65X102 ÷ 0.0138=72m

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