FE Exam Formulas Ch. 10 Flashcards
Purpose and Variables of…
Rational Formula
Q=peak rate of discharge (ft3/s)
C=runoff coefficient
I=rainfall intensity (in/hr)
A=drainage area (acres)
Purpose and Variables of…
Weighted Runoff Coefficient
C=runoff coefficient
A=drainage area (acres)
Purpose and Variables of…
Time of Concentration
Tc=time of concentration
L=flow path length
upsilon=flow velocity
Purpose and Variables of…
NRCS Curve Number Method
Q=runoff
P=precipitation
S=maximum basin retention
CN=curve number
Purpose and Variables of…
Maximum Basin Retention
S=maximum basin retention
CN=curve number
Purpose of…
Probability and Frequency Relationship
Purpose of…
Probability and Frequency Occurring in n years
Purpose and Variables of…
Probability of Storm/Flood Occurring in m CONSECUTIVE years
Purpose of…
Probability of Storm/Flood Not Occurring
Purpose and Variables of…
Continuity Equation
A=cross sectional area
v=velocity
Q=volumetric flow rate
Purpose and Variables of…
Manning’s Equation
v=velocity
K=1.486
n=Manning’s coefficient
Rh=hydraulic radius
S=slope of energy grade line
Purpose and Variables of…
Manning’s Equation for Flow Rate
Q=flow rate
A=flow area
v=velocity
K=1.486
n=Manning’s coefficient
Rh=hydraulic radius
S=slope of energy grade line
Purpose and Variables of…
Hydraulic Radius
Rh=hydraulic radius
A=flow area
P=wetted perimeter
Purpose and Variables of…
Minimum Pipe Diameter
D=pipe diameter
Q=volumetric flow rate
S=pipe slope
n=Manning’s coefficient
Purpose and Variables of…
Flow Rate
D=pipe diameter
Q=volumetric flow rate
S=pipe slope
n=Manning’s coefficient
Purpose and Variables of…
Velocity of a Pipe
D=pipe diameter
Q=volumetric flow rate
S=pipe slope
n=Manning’s coefficient
Purpose and Variables of…
Total Energy Head
y=flow depth
v=flow velocity
z=channel bottom elevation
Purpose and Variables of…
Specific Energy
y=flow depth
v=flow velocity
Purpose and Variables of…
Critical Depth
Q=discharge rate
g=acceleration due to gravity (32.2)
A=cross section area
T=width of water surface
Purpose and Variables of…
Critical Depth for Rectangular Channels
yc=critical depth
q=unit discharge=Q/B
g=acceleration due to gravity (32.2)
Purpose and Variables of…
Froude Number
Fr=froude number
v=velocity
g=acceleration due to gravity (32.2)
yh=hydraulic depth
Purpose and Variables of…
Hydraulic Jump
y1 and y2=conjugate flow depths upstream and downstream
Fr1=froude number at upstream supercritical flow location
Purpose and Variables of…
Specific Momentum
M=specific momentum
Q=flow rate
A=flow area
hhat=vertical distance from water surface to centroid of area
Purpose of…
Weir Formula
Purpose of…
Weir Formula
Purpose of…
Weir Formula
Purpose and Variables of…
Affinity Law
Q=volumetric flow rate
m=mass flow rate
H=head added by pump
P=pressure added by pump
W=pump input power
rho=fluid density
N=rotational speed
D=impeller diameter
Purpose and Variables of…
Affinity Law
Q=volumetric flow rate
m=mass flow rate
H=head added by pump
P=pressure added by pump
W=pump input power
rho=fluid density
N=rotational speed
D=impeller diameter
Purpose and Variables of…
Affinity Law
Q=volumetric flow rate
m=mass flow rate
H=head added by pump
P=pressure added by pump
W=pump input power
rho=fluid density
N=rotational speed
D=impeller diameter
Purpose and Variables of…
Affinity Law
Q=volumetric flow rate
m=mass flow rate
H=head added by pump
P=pressure added by pump
W=pump input power
rho=fluid density
N=rotational speed
D=impeller diameter
Purpose and Variables of…
Affinity Law
Q=volumetric flow rate
m=mass flow rate
H=head added by pump
P=pressure added by pump
W=pump input power
rho=fluid density
N=rotational speed
D=impeller diameter
Purpose and Variables of…
Waterpower
Wwater=waterpower
gamma=specific density
Q=volumetric flow rate
hpump=head increase provided by pump
Purpose and Variables of…
Pump Power
Wpump=power of pump
Wwater=waterpower
etapump=pump efficiency
Purpose and Variables of…
Motor Power
Wmotor=power of motor
Wwater=waterpower
etapump=pump efficiency
etamotor=motor efficiency
Purpose and Variables of…
Total Efficiency
etapump=pump efficiency
etamotor=motor efficiency
Purpose of…
Total Storage Volume
Purpose and Variables of…
Friction Head
hf=friction head
deltap=pressure loss
gamma=specific weight
Purpose and Variables of…
Darcy-Weisbach Equation for Laminar and Turbulent Flow
hf=head loss
f=Darcy friction factor
L=length of pipe
v=average velocity
D=internal pipe diameter
Purpose and Variables of…
Harzen-Williams Equation
hf=head loss
L=pipe length
C=roughness coefficient (Table 10.7)
D=pipe diameter
v=velocity
Q=discharge
k1=1.318
Rh=hydraulic radius
S=slope of energy grade line
Purpose and Variables of…
Harzen-Williams Equation
hf=head loss
L=pipe length
C=roughness coefficient (Table 10.7)
D=pipe diameter
v=velocity
Q=discharge
k1=1.318
Rh=hydraulic radius
S=slope of energy grade line
Purpose and Variables of…
Harzen-Williams Equation
hf=head loss
L=pipe length
C=roughness coefficient (Table 10.7)
D=pipe diameter
v=velocity
Q=discharge
k1=1.318
Rh=hydraulic radius
S=slope of energy grade line
Purpose of…
Total Friction Head Loss of Pipes in Series
Purpose of…
Friction Head Loss of Pipes in Series
Purpose of…
Total Friction Head Loss of Pipes in Parallel
Purpose of…
Friction Head Loss of Pipes in Parallel
Purpose and Variables of…
Discharge Flow from Sprinkler Head
Q=discharge flow
k=nozzle discharge coefficient
P=pressure
Purpose and Variables of…
Rated Capacity
QR=rated capacity
QF=total test flow
HR=PS-20psi
HF=PS-PR
PS=static pressure
PR=residual pressure
Purpose and Variables of…
Gutter Flow Rate
Q=flow rate
n=Mannings n
Sx=road cross slope
S=longitudinal slope
T=spread or top width
Purpose and Variables of…
Darcy’s Law
Q=discharge rate
K=hydraulic conductivity
A=cross sectional area of flow
h=hydraulic head
Purpose and Variables of…
Specific Discharge or Darcy Velocity
K=hydraulic conductivity
q=specific discharge
h=hydraulic head
Purpose and Variables of…
Seepage Velocity
K=hydraulic conductivity
q=specific discharge
h=hydraulic head
n=effective porosity
Purpose and Variables of…
Transmissivity
T=transmissivity
K=hydraulic conductivity
b=aquifer thickness
Purpose and Variables of…
Well Drawdown
Q=flow rate of water drawn from well
K=coefficient of permeability of soil or hydraulic conductivity
h1,h2=height of water surface above bottom of aquifer
r1,r2=radius to water surface at measurement
Purpose and Variables of…
Thiem Equation
Q=flow rate of water drawn from well
K=coefficient of permeability of soil or hydraulic conductivity
h1,h2=height of water surface above bottom of aquifer
r1,r2=radius to water surface at measurement
b=thickness of confined aquifer
h=height of piezometric surface prior to pumping
Purpose and Variables of…
Total Alkalinity
[HCO3-]=bicarbonate alkalinity
[CO3^2-]=carbonate alkalinity
[OH-]=hydroxide alkalinity
Purpose of…
Hardness
Purpose and Variables of…
Chemical Oxygen Demand
b=volume of FAS used in the blank sample
s=volume of FAS in the original sample
n=normality of FAS
Purpose of…
Mass Balance
Purpose and Variables of…
Steady State Mass Balance
M=mass
Min=mass in
Mout=mass out
r=reaction rate=kC^n
k=reaction rate constant (1/time)
n=order of reaction
C=concentration
Q=flow rates
V=volume
v=velocity
A=cross section area of flow
Purpose and Variables of…
Basic Mass Balance Equation
Purpose of…
Pounds Formula
Purpose of…
Water Supply Demand Quantity
Purpose and Variables of…
Population Projection - Linear Estimate
Pt=population at time t
P0=population at time zero
k=growth rate
deltat=elapsed time in years relative to time zero
Purpose and Variables of…
Population Projection - Exponential
Pt=population at time t
P0=population at time zero
k=growth rate
deltat=elapsed time in years relative to time zero
Purpose and Variables of…
Population Projection - Exponential
Pt=population at time t
P0=population at time zero
k=growth rate
deltat=elapsed time in years relative to time zero
Purpose and Variables of…
Population Projection - Percent Growth
Pt=population at time t
P0=population at time zero
k=growth rate
n=number of periods
Purpose and Variables of…
Projected Population Growth
P2=project population
P2R=projected population of a larger region
P1=population at last census
P1R=population of larger region at last census
k=growth ratio constant
Purpose and Variables of…
Rate of Annual Growth
Pt=population at time t
P0=population at time zero
k=growth rate constant
S=saturation population
Purpose and Variables of…
Terminal Settling Velocity
vt=terminal settling velocity
g=gravitational constant
rhop=density of particle
rhof=density of fluid
d=diameter of sphere
CD=drag coefficient
Purpose of…
Stoke’s Law
Purpose and Variables of…
Weir Overflow Rate
Q=flow rate
Purpose of…
Horizontal or Approach Velocity
Purpose and Variables of…
Hydraulic Residence Time
Q=flow rate
Ax=cross-sectional area
A=surface area, plan view
V=tank volume
Purpose and Variables of…
Filtration Equation - Monosized Media
hf=head loss through the clean bed
L=depth of filter media
eta=porosity of bed=void volume/total volume
vs=filtration rate=Q/Aplan
g=gravitational acceleration
Re=Reynolds number
d=diameter of filter media particles
Purpose and Variables of…
Filtration Equation - Multisized Media
hf=head loss through the clean bed
L=depth of filter media
eta=porosity of bed=void volume/total volume
vs=filtration rate=Q/Aplan
g=gravitational acceleration
Re=Reynolds number
d=diameter of filter media particles
Purpose and Variables of…
Carman-Kozeny Equation - Monosized Media
hf=head loss through the clean bed
L=depth of filter media
eta=porosity of bed=void volume/total volume
vs=filtration rate=Q/Aplan
g=gravitational acceleration
Re=Reynolds number
d=diameter of filter media particles
Purpose and Variables of…
Carman-Kozeny Equation - Multisized Media
hf=head loss through the clean bed
L=depth of filter media
eta=porosity of bed=void volume/total volume
vs=filtration rate=Q/Aplan
g=gravitational acceleration
Re=Reynolds number
d=diameter of filter media particles
Purpose and Variables of…
Friction Factor
f’=friction loss
eta=porosity of bed=void volume/total volume
Re=Reynolds number
Purpose and Variables of…
Depth of Fluidized Filter Media - Monosized
Lf=depth of fluidized filter media
vB=backwash velocity
QB=backwash flowrate
vs=terminal setting velocity
nf=porosity of fluidized bed
L0=initial bed depth
n0=initial bed porosity
Purpose and Variables of…
Depth of Fluidized Filter Media - Multisized
Lf=depth of fluidized filter media
vB=backwash velocity
QB=backwash flowrate
vs=terminal setting velocity
nf=porosity of fluidized bed
L0=initial bed depth
n0=initial bed porosity
Purpose and Variables of…
Porosity of Fluidized Filter Media
vB=backwash velocity
vs=terminal setting velocity
nf=porosity of fluidized bed
Purpose and Variables of…
Osmotic Pressure
PI=osmotic pressure
phi=osmotic coefficient
v=number of ions formed from one molecule of electrolyte
n=number of moles of electrolyte
V=specific volume of solvent
R=universal gas constant
T=absolute temperature
Purpose and Variables of…
Salt Flux Equation
Js=salt flux through the member
Ds=diffusivity of the solute in the membrane
Ks=solute distribution coefficient
C=concentration
deltaZ=membrane thickness
Kp=membrane solute mass-transfer coefficient
Purpose and Variables of…
Water Flux through Membrane
Jw=water flux through the membrane
Wp=coefficient of water permeation
deltaP=pressure differential across membrane
deltapi=osmotic pressure differential across membrane
Purpose and Variables of…
Ultrafiltration Equation
Jw=volumetric flux
epsilon=membrane porosity
r=membrane pore size
deltaP=pressure differential across membrane
deltapi=osmotic pressure differential across membrane
mu=viscosity
delta=membrane thickness
Purpose and Variables of…
BOD Loading Equations
k=BOD decay rate constant
L0=ultimate BOD
BODt=the amount of BOD exerted at time t
Purpose of…
Kinetic Temperature Corrections
Purpose of…
Calculating SVI
Purpose and Variables of…
Sludge Volume/Day
rhos=density of solids
M=sludge production rate
Purpose and Variables of…
Hydraulic Residence Time
Q=flow rate
V=tank volume
Purpose of…
Surface Overflow Rate
Purpose and Variables of…
Fixed Film Equation without Recycle
Se=effluent BOD5
S0=influent BOD5
R=recycle ratio
QR=recycle flow rate
D=depth of biotower media
Q=hydraulic loading
k=treatability constant
Purpose and Variables of…
Fixed Film Equation with Recycle
Se=effluent BOD5
S0=influent BOD5
R=recycle ratio
QR=recycle flow rate
D=depth of biotower media
Q=hydraulic loading
k=treatability constant
Variables of…
Se=effluent BOD5
S0=influent BOD5
R=recycle ratio
QR=recycle flow rate
D=depth of biotower media
Q=hydraulic loading
k=treatability constant
