FE Exam ReviewCivil Engineering

Hydraulics, Hydrology, and Fluid Mechanics

Cary Troy, Lyles School of Civil Engineering

February 11, 2015

Exam Specifications – Civil Engineering

http://ncees.org/wp-content/uploads/2013/10/FE-Civil-CBT-specs_with-ranges.pdf

http://ncees.org/wp-content/uploads/2013/10/FE-Civil-CBT-specs_with-ranges.pdf

Exam Specifications – Civil Engineering

Reference Manual

Runoff (Q) = Rainfall (P) - Losses

http://ncees.org/exams/study-materials/download-fe-supplied-reference-handbook/

RUNOFF

RAINFALL

Losses

Ground

Example: If 3” of rain fall on a catchment that has a curve number of 75, what is the total amount of direct runoff?

(depnds on catchment type, 0-100)

Peak runoff (discharge)

Rain falls at a maximum rate of 2”/hour on a watershed of 77 acres. If the runoff

coefficient is 0.42, what is the expected

peak discharge?

Flow

Time

QHydrograph

Groundwater flow

A given soil has hydraulic conductivity K=5 x 10-6 m/s. If the hydraulic grade line falls 1m every 100m of distance, what is the average seepage velocity? The effective porosity is 0.55.

Well drawdown

Well drawdown - unconfined

Well drawdown - confined

Open Channel Flow classifications

• Uniform vs. non-uniform• If Uniform, can use Manning’s equation

• If not, need to use specific energy to relate points at different locations

• Critical, vs. super-critical vs. sub-critical• Depends on the Froude number

• Fr>1 : Super-critical

• Fr<1 : Sub-critical

• Hydraulic Jump:• Flow jumps from super-critical (shallow) to sub-critical (deep)

Key variables

• Flow rate, Q (m3/s, cfs)

• Flow rate per unit width, q (m2/s, ft2/s)

• Average velocity, V = Q/A (m/s, ft/s)

Flow depth, y (m,ft)Channel width, B (m, ft)Flow area, A (m2, ft2)Wetted perimeter, P (m,ft)Hydraulic radius, RH = A/P (m,ft)

Specific Energy

Flow is always somewhere along this curve, for a given flowrate per unit width

Open Channel Flow – Uniform flow

• Manning’s Equation for Uniform Flow A 20 foot wide rectangular channel has a slope of 0.0001. If the channel has Manning’s n of 0.013, and the depth is 3ft, what is the discharge? Assume uniform flow.

Open Channel Flow – Froude number

An open channel flow has discharge 300 cfs. If the channel is rectangular with width 10ft, and the depth is 3ft, what is the Froude number of the flow? How would you classify the flow?

Open channel flow – critical flow/depth

• For a given flow rate and channel geometry, what is the critical depth of flow?

WeirsRectangular

H

L

H

V-Notch

Full (pressurized) pipe flow – Hazen Williams

Head loss in full pipes – H-W

Head loss in pipes – H-W

Partially-full pipe flow (sewers)• Calculate totally full

discharge, velocity

• Use depth ratio to figure out partially-full:• Discharge

• Velocity

• Other

Flow in open channels

• geometry: wetted perimeter, P, and hydraulic radius, Rh = A/P

• uniform flow: Sf = S0 , where S0 is channel slope

• concept of critical flow and importance of Froude number• for rectangular channels of width, B, and depth, y:

– subcritical flow (Fr < 1 or y > yc), supercritical flow (Fr > 1 or y < yc)

1/ 3

2/ , / , / , 1c cq Q B Vy y q g Fr V gy Fr

B

y

Open channel problems

• (p. 6, #3) What is the hydraulic radius of a rectangular flume 2 ft high and 4 ft wide, which is running half full?

/ /( 2 )hR A P By B y

21 / , /c c c c cFr V gy y V g

• (p. 6, #12) The critical depth in a rectangular channel 8 ft wide flowing at a critical velocity of 2 ft/s is approximately?

B

yAns: B D

Ans: A