if the head is very small, if the edge is well rounded, or if air cannot flow in beneath the nappe, this results in an increase in the discharge rate for a given head as compared with that for a free nappe
Narrow rectangular notches have been found to give about 93 percent of the discharge predicted by the Francis formula
For the flow of high-viscosity liquids over rectangular weirs, the discharge decreases markedly for a given head as viscosity is increased
For fluids of moderate viscosity, the effect of viscosity and surface tension on the discharge flow rate for rectangular and triangular-notch ( 45°) weirs can be neglected when (NR) 0.2 (Nwe) 0.6 > 900
Standards governing pumps and compressors
ASME Standards
API Standards
Hydraulic Institute Standards
NFPA Standards
Pumps and compressors
Used to deliver fluids from one location to another through conduits
Pump is used when the fluid is a liquid, compressor is used when the fluid is a gas
Primary means of transfer of energy to the fluid that causes flow
Gravity
Displacement
Centrifugal force
Electromagnetic force
Transfer of momentum
Mechanical impulse
Combination of these
Major types of pumps
Positive displacement
Dynamic (kinetic)
Lift
Electromagnetic
Displacement
Discharge of a fluid from a vessel by partially or completely displacing its internal volume with a second fluid or by mechanical means
Displacement-type fluid-transport devices
Adaptable to high-pressure operation
Flow rate is variable
Mechanical considerations limit maximum throughputs
Capable of efficient performance at extremely low-volume throughput rates
Centrifugal fluid-transport devices
Discharge is relatively free of pulsation
Mechanical design lends itself to high throughputs
Capable of efficient performance over a wide range of pressures and capacities even at constant-speed operation
Discharge pressure is a function of fluid density
Relatively small high-speed devices and less costly
Axial-flow compressor or pump
Combines the use of centrifugal force with mechanical impulse to produce an increase in pressure
Electromagnetic pumps
Use electromagnetic field around the fluid conduit to create a driving force that will cause flow
Jets and eductors
Deceleration of one fluid (motivating fluid) to transfer its momentum to a second fluid (pumped fluid)
Turbine or regenerative-type pump
Functions partially by mechanical impulse
Capacity
Mass rate of fluid flow through the pump/compressor
Head
Total pressure differential measured immediately before and after the pump/compressor, usually expressed in the height of column of fluid equivalent under adiabatic conditions
Pump capacity
The product of (1) the mass rate of fluid flow through it and (2) the total pressure differential measured immediately before and after the device, usually expressed in the height of column of fluid equivalent under adiabatic conditions
Capacity
The first of the two quantities that determine pump capacity, normally referred to as capacity
Head
The second of the two quantities that determine pump capacity, known as head
Capacity is expressed in cubic meters per hour (m³/h) for both liquids and gases in SI units, and in U.S. gallons per minute (gal/min) for liquids and in cubic feet per minute (ft³/min) for gases in U.S. customary units
Density or specific gravity must be used for conversion to mass rate of flow when using volume units for capacity
For gases, capacity must be related to a pressure and a temperature, usually the conditions prevailing at the machine inlet
All heads and other terms are expressed in height of column of liquid
Total Dynamic Head (H)
The total discharge head (ha) minus the total suction head (hs)
Total Suction Head (hs)
The reading (has) of a gauge at the suction flange of a pump (corrected to the pump centerline), plus the barometer reading and the velocity head (hvs) at the point of gauge attachment
Static Suction Head (hss)
The vertical distance measured from the free surface of the liquid source to the pump centerline plus the absolute pressure at the liquid surface
Total Discharge Head (hd)
The reading (hgd) of a gauge at the discharge flange of a pump (corrected to the pump centerline), plus the barometer reading and the velocity head (hvd) at the point of gauge attachment
Static Discharge Head (hsd)
The vertical distance measured from the free surface of the liquid in the receiver to the pump centerline, plus the absolute pressure at the liquid surface
Velocity
The relationship between the quantity flowing past a given point in a given time and the velocity of flow for incompressible liquids
Velocity Head
The vertical distance by which a body must fall to acquire the velocity v
Viscosity
The internal friction or internal resistance to relative motion of the fluid particles in flowing liquids
Viscosity of liquids usually decreases with rising temperature
Viscous liquids tend to increase the power required by a pump, reduce pump efficiency, head, and capacity, and increase friction in pipe lines
Friction Head
The pressure required to overcome the resistance to flow in pipe and fittings
Work Performed in Pumping
The energy imparted to the liquid in performing the service required of the pump, which must be accounted for
Pump Efficiency
The ratio of power output to power input, defined as (power output)/(power input)
When selecting pumps, it is necessary to know the liquid to be handled, the total dynamic head, the suction and discharge heads, and often the temperature, viscosity, vapor pressure, and specific gravity
In the chemical industry, pump selection is frequently further complicated by the presence of solids in the liquid and liquid corrosion characteristics requiring special materials of construction
Positive Displacement Pumps
Provide high heads at low capacities, suited for high-viscosity service and slurry