### Introduction

Fluid mechanics is a branch of science that deals with the study of fluids in static and motion and its effect on the surrounding like the outside boundary. There are many applications of fluid mechanics and some of these we encounter in our daily lives.

Some of these are pumps, turbines, water and wind mill, water flow in a faucet, blood flowing in our veins and many others that utilize a fluid. Fluid can be either liquid or gas. Because of the special characteristics like viscosity, compressibility, and weight, fluids are given extra room for studies to utilize more these characteristics for the application on our daily lives.

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One of the most common practical uses of fluid mechanics is the application of the principles in designing pumps and turbines. These machines are designed to utilize the unique properties of a fluid. Pumps and turbine are mechanical devices that are usually related to fluid power. Their main difference is how the work or power is being done to the machine.

Power is being used in a pump to provide the desired output while turbines are designed to provide work or power from a moving fluid. The work in a pump goes to the system has and has a negative value and positive work is produced from a turbine. Pumps and turbine are used in many application concerning on fluid power control.

## Review of Related Literature

There are two major categories of pump, the positive-displacement and the dynamic change pump. The positive displacement pumps forced the fluid along through volume change. The fluid used is forced into the inlet and is drawn from a discharge port through volume change. Examples of a positive displacement pump are piston pumps, gear pumps and the heart of a mammal. A piston pump uses the change in volume by the up and down stroke of the piston. As the fluid enters to the inlet port, the volume will reach to the maximum capacity and the piston will move upward forcing the fluid to exit through the exhaust port. While in a mammalian heart, as blood enter to the inlet veins, the blood is then forced out through the artery as the heart muscle squeezed. (White, 1999) There are many classifications of a positive displacement pumps. Examples are reciprocating pumps, and rotary pumps.

All positive displacement pumps deliver a pulsating or periodic flow as the cavity volume opens, trapped and squeezes the fluid. One of the good features why this kind of pump is usually used is that it can deliver the liquid regardless of the viscosity. (White, 1999)

Dynamic pump moves the fluid by conveying momentum increase through the use of blades or rotating vanes. It utilizes the kinetic energy from a fast rotating blades or a certain special design. One major difference to the positive displacement pumps is that there is no closed volume. Because the fluid will increase in momentum thus increasing in velocity and this increase in velocity will be used to produce higher pressure gradient from the outside system and exiting to the discharge port. (White, 1999)

A good feature of a dynamic pump is that it produces high flow rate compared to a positive displacement pump and much steady discharge. It also provides a continuous constant-speed variation of performance, from near-maximum pressure change at zero flow to zero pressure change at a maximum flow rate. One drawbacks of a dynamic pump is that it is ineffective when the fluid has high viscosity. Viscosity is a property of a fluid to resist flow. Higher viscosity means that it can resist more the flow of the fluid. Thus if a fluid has high viscosity, the performance of dynamic pump is lessen. Another disadvantages of dynamic pumps, it requires to be primed. This means that it needs to be filled with water before it can perform its duty. (White, 1999)

Centrifugal pumps are classified as dynamic pumps. These pumps are one of the most popular pumps used in many industries. Centrifugal pumps works with the use of a rotating blades called the impeller that is within a casing. The fluid enters to the impeller by axial movement, then is caught to the impeller blades and rotates tangentially and is discharged through the exit port radially. The fluid when rotating into the impeller experienced increase in the velocity and pressure. Pressure is again increased as the fluid decrease in velocity through the diffuser thus increasing in pressure. This is what needed or the purpose of a pump, to produce a high pressure at the exit port. (White, 1999)

There are many designs of impeller blades and these are categorized to give the specific characteristics. The blades of the impeller are usually designed as backward-curved, forward-curved and radial blades.

## Output Parameters

Assuming steady flow, the pump basically increases the Bernoulli head of the flow between point 1, the eye to point 2, the exit port. Neglecting viscous work and heat transfer, the head can be determined using the equation below:

H = [(p/ρg) + (V2/2g) + z]2 – [((p/ρg) + (V2/2g) + z]1 = hS -hf

where p is the pressure, ρ is the density of the fluid, g is the gravitational constant, V is the velocity, z is the altitude, hS is the head of the pump, hf is the head losses and H is the Bernoulli head.

Since V2 and V1 do not vary usually and the difference in altitude can be assumed the same, these differences can be negligible and the pressure head can be assumed:

p 2- p1 Δp

H = ——– = ———

ρg ρg

The power delivered to the fluid can be determined by multiplying the density of the fluid times the gravitational acceleration times the volumetric flow rate times the head difference. In mathematical expression;

Pw = ρgQH

This expression is usually known as the water horsepower. The power required to drive the pump is the brake horsepower (BHP) and can be calculated using the equation below;

BHP = ωT

where is the shaft angular velocity and T is the torque produced from the rotating shaft.

The efficiency of the pump can be determined using the ratio of the output over the input. Because of head losses as well as friction losses, Pw is usually lower than the input which is the BHP. Thus the efficiency of the pump is;

Pw ρgQH

η = ——- = ———-

BHP ωT

There are three kinds of efficiency that is important in determining the performance of a centrifugal pump. These are the volumetric, hydraulic and mechanical efficiency. The volumetric efficiency can be determined using the equation below;

Q

η v = ——–

Q + QL

Where QL is the losses due to leakages. The hydraulic efficiency has the mathematical expression;

hf

η h = 1 – —–

hs

where hf can be accounted as friction losses in the impeller’s eye. And the mechanical efficiency can be determine using the equation below;

Pf

η m = 1 – —–

BHP

where is the power losses due to friction from moving parts of the pump like bearings. These are the important factors to be considered to have higher efficiency. The variables used must be designed well so that to maximize the utilization of efficiency. (White, 1999)

## Pump Performance Curves

Pump performance curves were determined from purely empirical method. Extensive testing was done from different centrifugal pumps to produce a performance curve. The performance curve derived from centrifugal pumps can be used also on mixed-flow and axial-flow and compressors.

Performance curve was done at constant angular rotation of the shaft. The independent variable that was used is the volumetric flow rate while the dependent variables are head H, pressure drop Δp, and the brake horsepower BHP. Note that the units to be used must be in uniform, meaning if metric system is used all units must be in metric otherwise in English units.

Example of a performance curve of a centrifugal pump. The head is approximately remain constant at low discharge and then drops to zero at Q = Qmax. At this point, with the indicated speed and impeller size, the pump cannot anymore deliver fluid than Qmax. Another trend from the performance curve is that as the flow increases, the head decreases. Conversely, as the head of the pump approaches to zero, flow rate is expected to be maximum. The relationship between the head and the volumetric flow rate is called “rising characteristic curve.” (Rodrick V. Chima)

The efficiency η is always zero when there is no flow rate or when Qmax and and it reaches to maximum at about 0.6 Qmax. The designed flow rate will give the maximum efficiency. (Rodrick V. Chima)

For this pump, the performance curve can be seen in figure 2. a stable head-capacity can be observed on the given curve. It means that there is a certain head for a given volumetric flow rate. The maximum head is about 1.13 m. the maximum efficiency for the given pump can be estimated to be 40% for a given flow rate of 0.7dm3/s. it is important to remember that it is recommended that the efficiency curve must be flat as possible or maximize at lower flow rate. It also shows that the power curve is almost flat from the given condition. This is a good characteristic of the curve but the head curve significantly changes through the given conditions. (Rodrick V. Chima)

In choosing the right kind of pump, a performance curve is needed by the buyer. There are many factors to consider in choosing the right kind of pump. First to consider is what the purpose of the pump to be used is like if is it in irrigation purposes, or ventilation purposes. This is very important because each purpose has different properties that must possess by the pump so that the efficiency of using the pump can be attained. Some information that are important in choosing the right kind of pump is, the required or designed head, for a given volumetric flow rate or the other way around.

## Net Positive Suction Head

Net positive suction head is the required in the inlet of the pump to maintain the fluid in cavitating. It is in the inlet where suction occurs and in this area where low pressure is experienced.

pi vi2 pv

NPSH = —– + —– – —–

ρg 2g ρg

where are the inlet pressure and inlet velocity and is the vapor pressure of the fluid. It must

me important to be remembered that the right hand side of the expression must be equal or higher than the NPSH so that to minimize the chance of cavitation.

## Series and Parallel Pumps

If a pump provides the right discharge but has a little head, a possible solution is by connecting the two identical pumps in series connection. Like in electricity, series connection has constant current but different voltage. The same with pumps applications, to provide the right head, the two pumps that have low head must be connected in series so that to make higher head. In figure 3, the two heads add at the same flow rate to give the combined-performance curve. The two does not need to be identical at all times. They may be have different speeds but must have the same size of shaft. (White, 1999)

If the application of pumps needs higher or steeper head, the two pumps must be connected in series.

Another interesting characteristic of pumps is that they can provide the right amount of head and the right amount of discharge. But if the discharge is too little, you can connect two pumps to have higher discharge that has the same suction and inlet conditions. Another condition where parallel connection is done is delivery demand varies. This is when one pump at low flow and the second pump is used for the higher discharge. Both valves must have check valves. Check valves are engineering devices used in many water pumping system. It prevents the backflow of water. (White, 1999)

From figure 4, the pump does not require to be identical. Physically, their flow rates will be added up at the same head. In figure 4, point B has higher head than point A. pump A cannot be added in until the operating head is below the shutoff head of pump A. Since the curve rises at higher flow rate, higher flow rate can be experienced when the two flow rates are added. (White, 1999

### References

- Havens, P. Increasing Attic Ventilation Through Design of Rotary Ventilators
- Retrieved April 8, 2007, from http://utwired.engr.utexas.edu/siegel/ARE381E_S04/final%20project/Symposium/Havens.pdf
- Rodrick V. Chima. Centrifugal Pump Investigation. Retrieved April 8, 2007, from http://www.ews.uiuc.edu/~field/me310/2-Centrifugal%20Pumps-S07.pdf
- White, F. M. (1999). Fluid Mechanics (4th edition ed.): McGraw-Hill.