Santa Clara University Department of Civil Engineering CENG 140 Water Resources Engineering Spring 2013 1 Random Supplemental Data 1 acre = 43,560 ft 2 1 mi 2 = 640 acres = 2.78784 x 10 7 ft 2 1 m = 3.28 ft 1 m 3 = 1000 liters 1 km 2 = 10 6 m 2 1 m = 1000 mm 1 hectare=2.47 acres 1 inch = 2.54 cm = 25.4 mm Surface area of a sphere = 4πr 2 π=3.14159265358979323846 Diameter of the earth = 12,756 kilometers (at the equator) Relative humidity, R h =e/e s ; e = actual vapor pressure of the air. e≈e s 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: F P T − = = 1 1 1 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: KS X X + = Rational Formula Q=CiA (i in inches/hr, A in acres, Q in cfs; or i in m/s, A in m 2 , Q in m 3 /s) Bed Shear Stress o o yS γ τ = where γ=specific weight of water, y=flow depth and S o =bed slope Reservoir Storage Required=max(ΣI-ΣO) (maximum between peak and subsequent low value) Infiltration Trench Design: V in =Qt; V out =KHLt; V storage =WHLn Infiltration/runoff Equations: Horton NRCS ( ) kt c c p e f f f f − − + = 0 ( ) S P S P Q 8 . 0 2 . 0 2 + − = when P> 0.2S P, Q in length units I a =0.2S − = 10 1000 CN S α α=1 for S in inches, α=25.4 for S in mm.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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)
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) .