4–2 pressure-velocity-head...

4–2 PRESSURE-VELOCITY-HEAD RELATIONSHIPS

The association between quantity of water flow,

average velocity, and cross-sectional area

of flow is given by the equation

This formula is known as the continuity equation


For an incompressible fluid such as water:

If cross-sectional area decreases,

velocity of flow must increase

If the area increases, the velocity decreases


Total energy in a hydraulics system is equal to the sum

of elevation head + pressure head + velocity head


• Valves, fittings, and other appurtenances disturb

the flow of water, causing losses of head

– In addition to the friction loss in the pipe

• Distribution system losses due to appurtenances are

relatively insignificant compared to pipe friction losses

• In pumping stations & treatment plants, minor losses

in valves & fittings are a major part of the total losses


Unit head losses may be expressed as being

equivalent to the loss through a certain

length of pipe or by the formula

4–3 FLOW IN PIPES UNDER PRESSURE

The most common pipe flow formula used

in the design and evaluation of a water

distribution system is the Hazen Williams

4–4 CENTRIFUGAL PUMP CHARACTERISTICS

• Pumps do many jobs in water/wastewater systems

– Low-lift pumps elevate water from a source, or

wastewater from a sewer, to the treatment plant

– High-service pumps discharge water under pressure to a

distribution system, or wastewater through a force main

– Booster pumps to increase pressure in water distribution

systems, and are used for recirculation

– Transfer pumps move water within a treatment plant

– Well pumps lift water from shallow or deep wells

– Reciprocating positive-displacement and progressing

cavity pumps are used to move sludges


• Pumps do many jobs in water/wastewater systems

– Vertical turbine pumps are used for well pumping

– Pneumatic ejectors are used for small wastewater

lift stations

– Air-lift, peristaltic, rotary displacement, and turbine

pumps are used in special applications

– Other types are used for chemical feeding, sampling,

and fire fighting


• Centrifugal pumps are used for low and high service

to lift and transport water (Fig. 4–9)

• They are simple, compact, low cost, and operate

under a wide variety of conditions

• Essential parts are a rotating member with vanes,

the impeller, and a surrounding case


• The high speed impeller throws water into the volute

– which channels it through the nozzle to the discharge

• Depends partly on centrifugal force—hence the name

• A closed impeller is generally used in pumping water

for higher efficiency

– An open unit is used for wastewater containing solids


• Pump Head-Discharge Curve

– Head developed by a pump at various rates of discharge

and constant impeller speed is established by tests

(Fig. 4–10)

The head given is discharge pressure with

the inlet static water level at the elevation

of the pump center-line

Excluding suction and discharge piping losses


• A centrifugal pump is designed to operate near the

point of best operating efficiency

– Radial loads on the bearings are at a minimum

• As pump discharge increases beyond optimum, radial

loads increase, making cavitation a potential problem

• When discharge rates decrease toward shutoff head,

water recirculation in the casing can cause vibration

– And hydraulic losses

Discharge is directly

proportional to speed

Head is proportional to

the square of the speed

Power input varies with

the cube of the speed


A pump can be equipped with impellers of different

diameters for each size casing, in specific ranges

For a given impeller diameter at different speeds:

Discharge is approximately

proportional to speed

Head is proportional to

the square of the speed

Power input varies with

the cube of the speed


A pump can be equipped with impellers of different

diameters for each size casing, in specific ranges

For a given impeller diameter at the same speed:


Efficiency of a pump is the ratio of

power output to measured power input

Power input is the motor power applied to a pump

Power output is work done per unit of time

4–5 SYSTEM CHARACTERISTICS

• When a centrifugal pump lifts water from a reservoir

into a piping system, resistance to flow is described

by a system head curve

• The two components of discharge resistance are:

– Static head—elevation difference between water levels

in the suction reservoir and the point of discharge

– Friction head loss—which increases with pumping rate


• Constant-Speed Pumps

– Continuity of flow rate and water pressure must exist

at the common boundary between pump & piping

• A constant-speed pump operates at the head-

discharge point defined by the intersection of

the pump & system head-discharge curves

(Figs. 4–14 & 4–15)

• Pumping stations with two constant-speed pumps of

the same capacity may be used in small systems


• In larger systems, at least three pumps are desirable

to cover extremes of water demand

– And provide a standby in case one unit is out of service

• Since a larger system has continuous water demand,

pumps can discharge directly to the distribution piping

(Fig. 4–16)

– Elevated storage tanks are connected to the pipe network


• Variable-Speed Pumps

– Varying impeller rotational speed maintains constant

discharge pressure over a wide range of flow rates

• Pump discharge of a constant speed pump can be

controlled by a throttling valve in the pump outlet

– It causes water recirculation in the casing, reducing

efficiency and possibly damaging the bearings & impeller

• Centrifugal pump speed control of is achieved with

an electric motor designed for stepless speed drive


• Pump speed increases when discharge pressure

reduces as a result of increasing demand

– It decreases with increasing discharge pressure

• The transducer of a variable speed drive transfers the

signal from the pressure switches to the drive motor

A variable-speed drive must be prevented

from operating a pump at extremely low speeds


• When demand is under minimum required discharge,

the pump is protected by recirculating water

• Recommended minimum discharge rate is generally

25 - 35% of pumping rate at best operating efficiency

(Fig. 4–18)

• Variable-speed pumps can be operated in parallel in

multiple-pump installations

– Based on design, the pumps may function by load

sharing or staggered operation

4–6 EQUIVALENT PIPES

• An equivalent pipe is an imaginary conduit replacing

a section of a real system

– Head losses in the two systems are identical for flow

• Pipes of differing diameters connected in series can

be replaced by an equivalent pipe of one diameter

• Equivalent pipes cannot be applied to complex

systems—due to crossovers and withdrawal points


• Flows in pipes, head losses, and water pressures in

distribution systems are determined by computer

– Several mathematical programs have been developed

for computer analysis of water distribution systems

• The common choice is a steady-state simulation

– That represents the system for any prescribed set

of flow and pressure conditions

• An unsteady-state model simulates the behavior of a

system during a series of successive steps over time


• A computer program stores the pipe network as a

mathematically defined map, incorporating data on:

– Pipe lengths and diameters

– Roughness values (Hazen Williams C values)

– Pipe junctions (nodes) including elevations and

connecting pipes

– Check valves and pressure regulators

• Pipe roughness factors are assumed based on the

age of the pipe, and adjusted during model calibration


• A skeletal pipe network generally simplifies the

model with no loss of accuracy in analysis

• Storage reservoirs are defined by location in the

pipe network and their operating water level

• Pump characteristics are best determined by field

measurements under a range of discharge pressures

• Simultaneous measurements of the suction reservoir

or well casing are necessary to adjust pumping curves


• With the system modeled, water use data is added

– Assigning withdrawals at the nodes for a known condition

of water consumption

• Actual water consumption records from meter

readings provide the best data on water use


• The mathematical model must be calibrated to ensure

it represents the real system as closely as possible

• The procedure involves recording of flows, pressures,

and operational conditions for selected test days

• Preliminary calibration is done by measuring pressure

at various locations in the pipe network

– With distribution of withdrawals typical of average use


• Essential data include:

– Static pressure recordings at hydrants

– Elevations of water in reservoirs

– Discharge pressures & flow rates from pumping

stations and wells

– Flow measurements of meters in the distribution

system and at major water customers

• Calibration for pressure during average use may not

give accurate prediction in extreme conditions

– Such as fire demand, or maximum daily use


• The predictive capability of a model necessitates

collection/analysis of independent sets of data

– To avoid compensating errors in calibration/ verification


• A reliable computer model of a distribution system

has several advantages:

– System hydraulics can be evaluated for optimum

energy efficiency

– For periods of both low & high water demand, pumps

and wells can be analyzed for best operation

– Emergency situations, such as a major fire or main

break can be studied

– The effect of a potential major industrial customer can

be analyzed

4–8 GRAVITY FLOW IN CIRCULAR PIPES

• Sanitary and storm sewers are designed to flow as

open channels—not under pressure

• Storm sewers may occasionally be overloaded when

water rises in the manholes, surcharging the sewer

• Wastewater flows downstream by force of gravity

– Velocity of flow depends on steepness of the pipe

slope and frictional resistance

4–8 GRAVITY FLOW IN CIRCULAR PIPES

• The coefficient of roughness, n, depends on:

– The condition of the pipe surface

– Alignment of pipe sections

– Method of jointing

• After pipes are placed in use they accumulate grease

and other solids that disturb wastewater flow

4–2 pressure-velocity-head...

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