Computer Applications in

Hydraulic Engineering

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Academic CD

Aplikácie výpočtovej techniky v hydraulike pre inžinierov Flow Master General Flow Characteristic Všeobecná charakteristika prúdenia vody v otvorenom koryte

Flow Area prietočná plocha Wetted Perimeter omočený obvod

wPAR =

4.4/. 2 D

DDRcircular ==π

π

R hydraulic radius hydraulický polomer A cross-sectional area prietočná plocha Pw wetted perimeter omočený obvod

D pipe diameter priemer potrubia

pozdĺžny preirez (profil)

Depth hĺbka vody Velocity distribution rozdelenie rýchlosti

AQV =

V mean velocity, average cross-section velocity stredná rýchlosť, priemerná profilová rýchlosť Q flowrate, discharge prietok

laminárne prúdenie turbulentné prúdenie

νVDRe.

= ν

VRRe.4

=

Re Reynolds number Reynoldsovo číslo

ν kinematic viscosity kinematická viskozita Re < 2000 laminar flow laminárne prúdenie Re >4000 turbulent flow turbulentné prúdenie others laminar or turbulent flow ostatné laminárne alebo turbulentné prúdenie Example 1.1 A rectangular concrete channel is 3 meters wide and 2 meters high. The water in the channel is 1.5 meters deep, and is flowing at a rate of 30 m3/s. Determine the flow area, wetted perimeter, and hydraulic radius. Is the flow laminar or turbulent ? Energy Energia

Datum zrovnávacia hladina Energy Grade Line sklon čiary energie Hydraulic Grade Line sklon hladiny

LHg

VzpHg

Vzp+++=+++

22

22

22

0

21

11

γγ

p pressure tlak

γ specific weight merná tiaž z elevation kóta nad zrovnávaciou hladinou g gravitational acceleration konštanta gravitačného zrýchlenia H0 head gain, such as from a pump prírastok výšky, napr. pomocou pumpy HL combined head loss hladina kombinovaných strát Example 1.2 A 48-inch diameter transmission pipe carries 2,000 gallons per minute from an elevated storage tank a water surface elevation of 1,764 feet. Two miles from the tank, at an elevation of 1,423 feet, a pressure meter reads 85 psi. If there are no pumps between the tank and the meter location, what is the rate of headloss in the pipe ? Friction Losses Trecie straty Generalized velocity equation Zovčeobecnená rovnica pre výpočet rýchlosti

yxSkCRV = k factor to account for empirical constants, unit conversion faktor na započítanie empirických konštánt, konverzia jednotiek C flow resistance factor rýchlostný súčiniteľ S friction slope sklon čiary energie x,y exponents empirické hodnoty exponentov Manning’s Equation – open channel flow equation Manningova rovnica – rovnica pre prúdenie v otvorenom kanále

2/13/2 SRnkV =

k 1.49 for U.S. Standard units, 1.00 for S.I. units 1.49 pre U.S. Standard jednotky, 1.00 pre S.I. jednotky n Manning’s roughness value Manningov súčiniteľ drsnosti Chezy’s (Kutter’s) Equation – sanitary sewer design and analysis návrh a analýza stokových kanálov

RSCV = Kutter’s equation in S.I. units Kuttersova rovnica v S.I. jednotkách

R

ns

nSC⎟⎠⎞

⎜⎝⎛ +

+

++=

00155.0231

100155.023

Hazen-Williams Equation – design and analysis of pressure pipe systems návrh a analýza systémov tlakových potrubí

54.063.0 SkCRV = k 1.32 for U.S. Standard units, 0.85 for S.I. units 1.32 pre U.S. Standard jednotky, 0.85 pre S.I. jednotky C Hazen-Williams roughness coefficient Hazen-Williamsov súčiniteľ drsnosti

Tabuľka typických hodnôt súčiniteľa drsnosti Darcy-Weisbach (Colebrook-White) Equation - design and analysis of pressure pipe systems návrh a analýza systémov tlakových potrubí

RSfgV 8

=

f Darcy-Weisbach friction factor Darcy-Weisbachov factor trenia Free surface Voľná hladina

⎟⎟⎠

⎞⎜⎜⎝

⎛+−=

fRRk

f e

51.212

log21

Full Flow (Closed Conduit) Plne prietočný profil (uzavreté potrubie)

⎟⎟⎠

⎞⎜⎜⎝

⎛+−=

fRRk

f e

51.28.14

log21

k roughness height drsnostná výška Re Reynolds Number Reynoldsovo číslo Example 1.3 Use the FlowMaster program to compare headloss computed by the Hazen-Williams equation to the headloss computed by the Darcy-Weisbach equation for a pressure pipe having the following characteristics : cast iron pipe (new) one mile in length, 12” in diameter at a flowrate of 1200 gallons per minute (with water at 65oF). Example 1.4 A concrete trapezoidal channel has a bottom with of 4meters and 45o sideslopes. If the channel is on a 1 % slope and is flowing 1 meter deep throughout its length, how much flow is being carried (use Manning’s equation) ? How much flow would the same channel carry if it were it were squared off at 4 meters instead of trapezoidal ? Specific Energy and Critical Flow Špecifická energia a kritické prúdenie

Channel Depth hĺbka kanála Critical Depth kritická hĺbka

gVyE2

2

+=

E specific energy špecifická energia y depth of flow hĺbka toku

Froude number gDVF =

Froudovo číslo D hydraulic depth D=A/T Hydraulická hĺbka T top width of flow Šírka toku v hladine F<1 subcritical flow Podkritické prúdenie – riečne prúdenie F>1 supercritical flow Nadkritické prúdenie – bystrinné prúdenie F=1 critical flow Kritické prúdenie

gQ

TA 23

=

Example 1.5 What is the critical depth for a grassy triangular channel with 2H:1V sideslopes and a 0.5% slope when the flow is 3 m3/s ? If the channel is actually flowing at 1.2 meters deep, is the flow critical, subcritical, or supercritical ?