Equation Selection and practice exam items Flashcards
What is the total energy in the pipe?
Given diameter, elevation, pressure in pipe
energy equation
H=(P/y) +(v2/2g) +Z
Convert psi to pressure head
P/y = (psi)(ft/psi) = final unit is FT
V =
Q/A
What Equations are used to solve the pressure in one tank, when two pressurized tanks are connected?
two energy equations left side is tank 1 right side is tank 2
(p/y)+(v2/2g) +Z = (p/y)+(v2/2g) +Z + losses ( hm+Hf)
What does it mean when minor losses are negligible?
Hm =0
this is used in the energy equation
How do you calculation friction loss given a βCβ?
hf is the goal and
hazen williams can be used if βcβ is given
hf= (3.022V^1.85L)/(c^1.85)(D^1.165)
What is the difference between Pound-force and Pound -mass
the weight of the mass unit (pound-mass) on Earthβs surface is approximately equal to the force unit (pound-force). This is convenient because one pound mass exerts one pound force due to gravity.
equivalent
Equation for total factored load
Wu = 1.2 (deadload) + 1.6 ( live load)
Find Total deadload (not factored )
When given
Selfweight load/ft
Dimensions of structure (beam)
Applied dead load
Weight of self ( length in feet) + dead load
What is the relationship between steel area to cross section area ratio
0.01<pg< 0.08
pg is,
How to determine minimum steel area
Determined by multiplying gross area of column by pg ratio (0.01)
As minimum = total cross section X 0.01
Determine the load capacity the reinforced concrete column will require
First calculate factored load,
1) Pu= 1.2 DL + 1.6LL
The required nominal capacity must be greater than the factored load
2) PN= Pu/ o
βoβ is a Greek letter, itβs basically a safety factor dependent on the column situation; ie for a column with tied supports o= 0.65
How to solve for deflection and what each variable meansEDIT THIS
Deflection= (FL)/(EA)
Where:
F=Force
L=Length
E?
A=cross sectional area?
Moment of inertia for a column with a rectangular cross sectionEDIT HORIZONTAL VS VERT
Ix=(bh^3)/12
B and h are cross sectional dimensions
Calculate bending stress at some point on a beam
&= (My)/I
Where& is actually a sideways 6 for bending stress
M= the bending moment
I= the moment of inertia of the beam
y= distance from neutral axis to the top &bottom of the beam extreme surfaces (ie. at the neutral axis y=0 )
What is a basic mass balance equation
INPUT-OUTPUT-COMSUMPTION = ACCUMULATION
What is headloss in valve?
Give discharge, Butterfly valve, 30 -in pipe and minor loss coefficient?
hL= (KL * V^2)/2g
*solve for V with Q
*Area with pipe diameter given
see handbook page
( similar to Entrance Head loss page 361) - search head loss
(page 330) for fittings/valves elbows
HL(or Hf) = C* (v^2)/2g
(C is KL) here
find by searching for minor head loss coefficient
What is the depth of discharge over a weir, 90-degree v-notch
given Flow and coefficient of discharge
Q= CXH^(5/2)
solve for H
(search v-notch, or v-notch weir)
this is the 90degree v-nmtch Cone equation
see page 321
What is the depth of discharge over a weir, 90-degree v-notch only given FlowCHECK
Q= CXH^(5/2)
solve for H
** how to determine C if not given =
(search v-notch, or v-notch weir)
this is the 90degree v-nmtch Cone equation
see page 321
what is the basic charge pattern (based on the periodic table columns)
+1,2,3,4,5- ( rows 6-9 unknown) , +2+2+2 +3, (sus)-3, -2,-1, 0
Equation for Compressive strength, and were to find it
fβc = P/A
Load (maximum failure load) / Cross Sectional Area
basically the same equation as 1.6.2.6 (stress on a cross section)
N-value of a layer, given a boring log and blow counts for a layer
This equation is not given - given 4 rounds ( and the number of blows required to reach the layer i.e. 12/15)
you add the number blows for the 2nd and 3rd rounds
basic equation to find Station PT? on a horizontal curve?
station PT = Station PC +L (not given)
basic equation to find station PC?
Station PC = Station PI - T
For a horizontal curve - the internal angle (d) of the triangle *** add picture = what to I angle
I= d/2
given in the visual picture of horizontal design
relation ship of Chord, Radius, and Internal angle of a horizontal curve
R = L/2(sin(I/2)) - not given
(page 281) Chord length = 2R Sin(I/2)
Horizontal Curve* Design - equation for Length of Curve and the Trick to use the equation
L = (RIΒ°pi)/180
Trick is the I internal angle must be in degrees
Radian to Degrees conversion
1 radian = 57.3 degrees
given a triangle ratio of X:Y (horizontal and vertical) and the vertical dimension, how do you use the ratio to solve for the horizontal dimensionCHECK
Vertical dimension multiplied by (X/Y)
the dimension plane u want is the ratio on top *** add picture
how do you solve for Book valve? what equation and what trick needs to be used.
first solve the straigh-line depreciation (Dj)
DJ= (c-S)/n
(n = total years given)
next you take the
original cost - (amount of years you want the book value for)*Dj
the trick here is it can have a 10 year depreciation, so THEN solving for Dj you use ten but then when u plug into the BV equation, ( or next step) you use the years from what the questions asks ( ie depreciates for 10 years what is BV in 8 years)
Explain how to solve LOG problems
Log (subscript A)(X)=B
equals
basic formula of log is
Log (subscript A)(X)=B
equals
X=A^B
effective stress/pressure basic equation - (geotech)
two layers of soil with no water table
π=π1H1+π2H2
Total Stress/pressure (geotech)
πβ=π-π
Total Stress = effective stress - pore water pressure
effective stress/pressure basic equation (Geotech)
no water table, 2 layers of soil and Surcharge given
π= S+ π1H1+π2H2
Primiarly Consolidation settlement - βnormally consolidated soilsβ
sc = (cc)/(1+e0) H0 log10(pf/p0)
equation # 3.2.1
Primiarly Consolidation settlement - βnormally consolidated soilsβ how to solve for π0
this is not given -
π0=π =π(H/2)
You consider the entire thickness of the compressible soil layer for computation
but for the π0=π you use h=1/2H because overburdern pressure is deteremined at the midpoint og the compressible layer
What is the horizontal length and how is it calulated
14 X (3/2) =
Ylength *(X/Y) = Xlength
The effective bearing capacity would be based on buoyant unit weight, also referred to as effective unit weight
Effective unit weight = saturated unit weight - unit weight of water
long term settlement for case 1 is less than Case 2 because clay is subject to long -term settlement
because the structure is cantilevered, in addition to the wind, dead load and live load will contribute to uplift (C)
Ix is maximum for this section by inspection, or calculcate Ix=Ad^2 for each section
D
A
Rushing erosion is not a stormwater erosion classification
select all flow profiles representing super critical flow
select all flow profiles representing super critical flow
select all flow profiles representing super critical flow
something erong onthis one ***
Points B and E are the two high points in the line with exception of the tank, which vents to the atmosphere and does not need an air release valve
Determine the flow transfered to the water in a mixer - given Q MDG, temperature and X second retention time, and velocity gradient
use Mean gradient equation
step one is solve for Volume using the hydraulic retention time
HRT = V/Q
plug in to equation and solve for P
HRT =
Given a aquifer with 3 layers each with a thickness and hydraulic conductivity given; what is the transmissivity of the aquifer?
knowing the handbook gives you the solution to solve Transmissitivty = Kb ( conductivity times thickness)
for an aquifer with three ( or more layers just solve the Transmissivity for each layer then add them all togther for the total Transmissivity
For an unconfined aquifer the elevation of the water table is observed to be A ft
the elevation of the base (bottom) of the aquifer is B, the hydraulic conductivity is C (ft/hr)
what is the thickness of the aquifer? how is it solved
The thickness of the aquifer is difference between the water table elevation and the bottom of the quifer
ie. ( A - B )= thickness
An observation well is located B feet from the pump well
The water table elvation is C feet
A second observation well is located D ft from the pumped well
the water table elevation is E ft
The base of the aquifer is at elevation F ft
and the hydraulic conductivity = A ft/day
How do you solve H1 and H2 for the Discharge equation ??
H1 = C - F
water table elevation of the observation well minus the bottom elevation
H2 = E- F
water table elevation of the second well minus bottom elevation
An observation well is located B feet from the pump well
The water table elvation is C feet
A second observation well is located D ft from the pumped well
the water table elevation is E ft
The base of the aquifer is at elevation F ft
and the hydraulic conductivity = A ft/day
How do you solve r1 and r2 for the Discharge equation ??
r1 = B
distance from the pump well
r2 = D
distance from the pump well
a soil with hydraulic conductivity of K is subjected to hydraulic gradient of B meter/ meter
If the area through which flow occurs is C (m^2)
To solve for discharge, what equation do you use and plug in these variables
Q= KC B
ie. dh/dx = hydraulic gradient
what is the equation for specific discharge through an unconfined aquifer ?
see highlight, note that specific discharge is different thatn discharge, but the only difference in calculation is no Area in the equation
An unconfined aquifer - Transmissivity of Z ft/day and thickness Y
Two observation wells are J feet apart, the water levels are W and V above the datum
When solving for specific discharge, how do you get (dh/dx)?
plug in variables for this problem
dh = W - V
the two water levels of the wells
dx = J
the distance between the two wwells horizontally
when a questions asks for the flowrate of water of width perpendicular to flow through the aquifer - what are they asking for and what equation do you use ?
Darcyβs Law Discharge
what is the equation for the elastic section modulus ? and how can it be used to solve stress in beam
Solve unit weight of concrete beam with a given cross section
- list an assumption that may need to be made
self weight of concrete = unit weight of concrete * cross section area
unit weight of concrete can be assumed to be 130 - 150 lbs./cu. if not given
horizontal centroid is what variable?
what is is the formaula for a rectangle cross section , with width = b and height = h
xc
for rectangle b/2
How do you solve angle of friction for a soil that underwent a triaxial shear test
- well drained, normal stress on failure plane and stress on the failure plan given?
Use the equation with the c=0 and reverse by using ARCTAN to solve for the angle
How to convert something to βstationβ format
divide by 100 and convert the β.β to β+β
ie 1234.987
123+49.87
when calculating βLβ - arc length
R must be in what units?
Feet,
not miles/ KM etc this is not stated on the handbook
PVC station =
PVC station = PVI station - (L/2)
not given
How to solve the station of the max elevation on the vertical curve? ( vertical curve)
PVC station +Xm = the station of the max elevation on the vertical curve
(Xm is given but this equation is not given)
the elvation of PVT is ?
(Back tangent elevation at the same point at the horizontal distance from PVC as PVT) + y
this is not given
equation for the elevation of the point at the same horizontal distance PVC as PVT but on the back tangent line
PVC elevation +g1(L)
what does it mean when when X = Xm on a crest vertical curve?
when x=xm that is the maximum curve elevation
highway capacity is
maximum flowrate
Can highway capacity be calculated with density and space mean speed?
NO the capacity is maximum flow
how to solve solve for wall thickness of a metal pipe given
outer diameter ( not inner) and axial loading and also allowable compressive strength
first use compressive (π) stress and axial loading (P) to solve for cross section area
π=P/A
next use the pipe section area to solve for inner diameter
(see image )
last use the outter diameter and inner diameterto solve for thickness
D outer = D inner +2X thickness
how to solve for thickness of pipe if outer diameter and inner diameter is given?
D outer = D inner +2X thickness
effective stress/pressure basic equation (Geotech)
2 layers of soil, water table starts the middle of layer #2
π= π1H1+π2H2 - πwater (H2/2)
Two pipes converge to one junction box then to a single pipe. Steps to find minimum size of the third pipe
NCESS 21
Arithmetic mean method for 11 rain gauges, solve average precipitation
NCESS 22
Rational method to determine max runoff method, given IDF CURVE AND RUNOFF COEFFICIENT
NCESS 23
Tangent slope at a given station for a horizontal sag curve
NCESS 28
Minimum horizontal distance from toe of the dam to face of structure per osha excavation requirements
Given type B SOIL
NCESS 39
Given a boom length, and minimum stand off distance, what is the maximum distance from the edge of the building that the load can be placed on the roof.
- solve for hypotenuse
- solve for the angle from the boom
- plug in the actual boom length
- solve for the X or y plan based on the question
for this one make sure to subtract the distances that are not included
Axial force resisted by a braces wall
NCESS 7
Determine the passive lateral resistance per unit length of wall
- solve the failure angle,
failure angle = 45-(rankine angle/2) - solve Ka
- Use Ka to solve Pa
- Use Pa to solve the triangle (the force against the wall)
1/2Paheight = resistance per length of wall
Calculate the moment the lateral earth pressure resultant produces on a retaining wall
- Solve Ka
- use Ka to solve Pa
- Use Pa to solve for β force or resultantβ which is the area of the triangle
- Solve the moment
the βforce or resultantβ acts on the triangle at (1/3) height
so Ma = Force * (1/3 height)
True or false- Effective pressure = SURCHARGE + effective stress
(When given surcharge)
True
For a reinforced concrete beam, Solve for steel bar size
Given Max factored moment, cross section, depth of compression block, effective depth, fy and fβc,
- Solve for the Mn, here you are given Mu so you must divide by the saftey factor,
*** use 0.90, for an unknown reason this is what is used - Use the equation for Mn to solve As ( area of steel)
- Use As to solve for Area of each bar, by dividing by # of bars in beam
β this might not be directly stated but from a picture you can count the βcirclesβ - Given Area of each bar, you go to the Bar table, if the area is between two sizes size up the bar to be conservative
Minimum steel area for a RC COLUMN & and the load capacity
- determine the minimum required steel area for the column - this relationship is not given you have to memorize
- use the relation ship to solve for As min-m pg=0.01 for minimum
- for part 2 of this problem, you use the load factor to get ultimate factored load
- solve for Pn, by dividing the factored load by the factor of safety
*** for this column with tied reinforcements factor of safety = 0.65
Effective depth of reinforcement
- list assumptions and tricks
GIVEN: Maximum moment, length of cantilever beam, fy and fβc and reinforcement ratio.
- the first assumption you have to make is that the max moment is already factored
- so solve for Mn with the saftey factor = 0.9 - Solve for βAstβ by using the given reinforcement ratio and calulcate gross area by the concrete cross section
- use Ast (this equals βAsβ) to solve fore βaβ
- Use the βMnβ calculcated to solve fore βdβ
5.Check/ Trick - plug the sovled βdβ into the steel reinforcement ratio given to see if equals.
Gallons of water needed to meet subbase moisture content and dry density requirement
Given lab tests moisture % and length of road
- gallons of water needed per station = Desired dry density X ( compacted cubic feet of soil/ 8.33* lb/gal) X ( Goal water content% - Exisiting water content %)/100
- Gallons per station/(W L )
- unsure on this
For a 90 degree weir - what is the C coefficient
2.54
lime needed to remove carbonate hardness
(equation not given)
Lime= CO2 +Bicarbonate + Magnesium to be removed + excess
(excess means excess lime)
For the design of an elevated potable water table - what design parameters are needed for each varible
