Computer Applications in Hydraulic Engineering

Transcription

1 Computer Applications in Hydraulic Engineering Academic CD Aplikácie výpočtovej techniky v hydraulike pre inžinierov Flow Master General Flow Characteristic Všeobecná charakteristika prúdenia vody v otvorenom koryte Flow Area Wetted Perimeter prietočná plocha omočený obvod R A P w π. D / 4 R circular π. D D 4 R hydraulic radius hydraulický polomer A cross-sectional area prietočná plocha P w wetted perimeter omočený obvod

2 D pipe diameter priemer potrubia pozdĺžny preirez (proil) Depth Velocity distribution hĺbka vody rozdelenie rýchlosti Q V A V Q mean velocity, average cross-section velocity stredná rýchlosť, priemerná proilová rýchlosť lowrate, discharge prietok laminárne prúdenie turbulentné prúdenie DV. R e ν 4RV. R e ν R e Reynolds number Reynoldsovo číslo

3 ν kinematic viscosity kinematická viskozita R e < 000 R e >4000 others ostatné laminar low laminárne prúdenie turbulent low turbulentné prúdenie laminar or turbulent low laminárne alebo turbulentné prúdenie Example 1.1 A rectangular concrete channel is 3 meters wide and meters high. The water in the channel is 1.5 meters deep, and is lowing at a rate o 30 m 3 /s. Determine the low area, wetted perimeter, and hydraulic radius. Is the low laminar or turbulent? Energy Energia Datum Energy Grade Line Hydraulic Grade Line zrovnávacia hladina sklon čiary energie sklon hladiny p1 V1 + z1 + + H γ g 0 p + z γ V + + g H L p pressure tlak

4 γ z g H 0 H L speciic weight merná tiaž elevation kóta nad zrovnávaciou hladinou gravitational acceleration konštanta gravitačného zrýchlenia head gain, such as rom a pump prírastok výšky, napr. pomocou pumpy combined head loss hladina kombinovaných strát Example 1. A 48-inch diameter transmission pipe carries,000 gallons per minute rom an elevated storage tank a water surace elevation o 1,764 eet. Two miles rom the tank, at an elevation o 1,43 eet, a pressure meter reads 85 psi. I there are no pumps between the tank and the meter location, what is the rate o headloss in the pipe? Friction Losses Trecie straty Generalized velocity equation Zovčeobecnená rovnica pre výpočet rýchlosti V kcr x S y k C S x,y actor to account or empirical constants, unit conversion aktor na započítanie empirických konštánt, konverzia jednotiek low resistance actor rýchlostný súčiniteľ riction slope sklon čiary energie exponents empirické hodnoty exponentov Manning s Equation open channel low equation Manningova rovnica rovnica pre prúdenie v otvorenom kanále k V n R / 3 S 1/

5 k n 1.49 or U.S. Standard units, 1.00 or S.I. units 1.49 pre U.S. Standard jednotky, 1.00 pre S.I. jednotky Manning s roughness value Manningov súčiniteľ drsnosti Chezy s (Kutter s) Equation sanitary sewer design and analysis návrh a analýza stokových kanálov V C RS Kutter s equation in S.I. units Kuttersova rovnica v S.I. jednotkách C S n n s 1+ R Hazen-Williams Equation design and analysis o pressure pipe systems návrh a analýza systémov tlakových potrubí V kcr 0.63 S 0.54 k C 1.3 or U.S. Standard units, 0.85 or S.I. units 1.3 pre U.S. Standard jednotky, 0.85 pre S.I. jednotky Hazen-Williams roughness coeicient Hazen-Williamsov súčiniteľ drsnosti

6 Tabuľka typických hodnôt súčiniteľa drsnosti Darcy-Weisbach (Colebrook-White) Equation - design and analysis o pressure pipe systems návrh a analýza systémov tlakových potrubí V 8g RS Darcy-Weisbach riction actor Darcy-Weisbachov actor trenia Free surace Voľná hladina 1 k.51 log + 1R Re Full Flow (Closed Conduit) Plne prietočný proil (uzavreté potrubie)

7 1 k.51 log R Re k R e roughness height drsnostná výška 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 or a pressure pipe having the ollowing characteristics : cast iron pipe (new) one mile in length, 1 in diameter at a lowrate o 100 gallons per minute (with water at 65 o F). Example 1.4 A concrete trapezoidal channel has a bottom with o 4meters and 45 o sideslopes. I the channel is on a 1 % slope and is lowing 1 meter deep throughout its length, how much low is being carried (use Manning s equation)? How much low would the same channel carry i it were it were squared o at 4 meters instead o trapezoidal? Speciic Energy and Critical Flow Špeciická energia a kritické prúdenie Channel Depth Critical Depth hĺbka kanála kritická hĺbka

8 V E y + g E y speciic energy špeciická energia depth o low hĺbka toku Froude number Froudovo číslo F V gd D hydraulic depth DA/T Hydraulická hĺbka T top width o low Šírka toku v hladine F<1 subcritical low Podkritické prúdenie riečne prúdenie F>1 supercritical low Nadkritické prúdenie bystrinné prúdenie F1 critical low Kritické prúdenie A T 3 Q g Example 1.5 What is the critical depth or a grassy triangular channel with H:1V sideslopes and a 0.5% slope when the low is 3 m 3 /s? I the channel is actually lowing at 1. meters deep, is the low critical, subcritical, or supercritical?