water resources final equation sheet
DESCRIPTION
Water ResourcesTRANSCRIPT
Santa Clara University Department of Civil Engineering
CENG 140 Water Resources Engineering Spring 2013
1
Random Supplemental Data 1 acre = 43,560 ft2
1 mi2 = 640 acres = 2.78784 x 107ft2
1 m = 3.28 ft
1 m3 = 1000 liters
1 km2 = 106 m2
1 m = 1000 mm
1 hectare=2.47 acres
1 inch = 2.54 cm = 25.4 mm
Surface area of a sphere = 4πr2
π=3.14159265358979323846
Diameter of the earth = 12,756 kilometers (at the equator)
Relative humidity, Rh=e/es ; e = actual vapor pressure of the air. e≈es at dew point temperature
Weibull plotting position (prob. of exceedence, P): m/(N+1), m=rank; N=total number
P(either A or B) = P(A) + P(B) (if A and B are independent and mutually exclusive)
P(both A and B) = P(A) x P(B) (if A and B are independent)
P(not A) = 1 - P(A) or (Prob. of exceedence) = 1 – (Prob. of non-exceedence)
P(no occurrences of A in any of N time periods) = (1 – P)N where P is the probability of any one
event occurring (probability of exceedence)
P(one or more occurrence in N time periods) = 1-(1-P)N
Return Period T: FP
T−
==1
11 where P=prob. of exceedence; F=prob. of non-exceedence
Residence time = Volume/Σ(inflows)
Standard Normal Deviate, z = (x-µ)/σ
Mass (Volume) Balance: I – O = dS/dt ≈ ∆S/∆t I=inflow O=outflow Standard flood frequency analysis equation: KSXX +=
Rational Formula Q=CiA (i in inches/hr, A in acres, Q in cfs; or i in m/s, A in m2, Q in m3/s)
Bed Shear Stress oo ySγτ = where γ=specific weight of water, y=flow depth and So=bed slope
Reservoir Storage Required=max(ΣI-ΣO) (maximum between peak and subsequent low value)
Infiltration Trench Design: Vin=Qt; Vout=KHLt; Vstorage=WHLn
Infiltration/runoff Equations: Horton NRCS
( ) ktccp effff −−+= 0 ( )
SPSPQ
8.02.0 2
+−
= when P> 0.2S P, Q in length units
Ia=0.2S
−= 101000
CNS α
α=1 for S in inches, α=25.4 for S in mm.
Santa Clara University Department of Civil Engineering
CENG 140 Water Resources Engineering Spring 2013
2
Equations for time of concentration (length L in m, slope S0 is unitless, time units as noted): Kirpich
385.00
77.0
019.0(min)SLtc =
Kerby
467.0
0
44.1(min)
=
SLrtc
NRCS
Sheet Flow: ( )4.0
05.0
2
8.0
0288.0(hrs)SP
nLts =
Overland/Concentrated Flow: sc
sc VLt =
where 5.00kSVsc =
Kinematic Wave
6.0
04.0
99.6(min)
=
SnL
itc where i is in mm/h
solved for i: 5.1
05.2
129
=
SnL
ti
c
Santa Clara University Department of Civil Engineering
CENG 140 Water Resources Engineering Spring 2013
3
Note: F(-z) = 1 – F(z)
Values in table are F(z), vertical axis is z to one decimal, columns are for the second decimal place.
Santa Clara University Department of Civil Engineering
CENG 140 Water Resources Engineering Spring 2013
4
Unit peak discharge for SCS rainfall distribution type I, used in TR-55 graphical peak flow formula.
Santa Clara University Department of Civil Engineering
CENG 140 Water Resources Engineering Spring 2013
5
NRCS TR-55 equations: SI a 2.0=
α=1 for S in inches, α=25.4 for S in mm. NRCS TR-55 graphical peak flow equation: Qp=quAQF where A is basin area, F is pond/swamp factor, and qu unit peak flow. For Central/Southern California, assume a Type 1 rain distribution, so qu can be determined from the figure above. Muskingum method: ( )[ ]111 1 OXXIKS −+= = K[weighted flow] 1211202 OCICICO ++=
( )( ) ( )K
tX
XKt
C∆+−
−∆=
12
20
( )( ) ( )K
tX
XKt
C∆+−
+∆=
12
21
( ) ( )( ) ( )K
tXK
tXC
∆+−
∆−−=
12
122
Storage indication equation: ( )
−
∆++=+
∆ −−
− 11
122
tt
tttt O
tS
IIOt
S
111
11 2
22−−
−−
− −
+
∆=−
∆ ttt
tt OO
tS
Ot
S
Darcy’s Law and groundwater hydraulic head
LhKV
LhKAQ ∆
=∆
= or Hydraulic head, h ≈ EGL elevation = γPz +
Actual velocity Vactual = V/n where V=“Darcian velocity,” determined from Darcy's law. n=porosity. Reservoir Trap Efficiency
−= 101000
CNS α
( ) 8.02.0 2
SPSPQ
+−
=when P> 0.2S (P, S, Q have same units)
Santa Clara University Department of Civil Engineering
CENG 140 Water Resources Engineering Spring 2013
6
NRCS Curve Number Adjustment
Shields Diagram:
x-axis: R*=U*ds/ν where ds=mean particle diameter (d50, the diameter for which 50% is finer by weight) , ν=kinematic viscosity of water. U*=(τo/ρ)½ where ρ is the density of water. y-axis: τ*=τo/[(γs-γ)ds] where γs=specific weight of the sediment material (for sand: γs =2.65γ) .