Julius Weisbach

7/23/2019 Julius Weisbach

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Julius Weisbach

Julius Weisbach was a German mathematician and engineer and was born on the 10th august

1806 , the eight of nine children to Christian Weisbach and Christina Rebekka Stehen in

!ittelschmiedeberg now called !ildenau municialit" # Weisbach recei$ed his initial

education at the %"ceum in &nnaberg and the 'ergschule in (reiberg#%n 18)) he decided to attendthe 'ergakademie where he later went on to Gottingen sending aro*imatel" two "ears , he

then followed in the footste of associate (riedrich !ohs to the +echnical ni$ersit" and

ni$ersit" of -ienna where he ursued mathemathics , h"sics and mechanics #'etween the

eriod of 18.1 to 18./ he acceted the resonsibilit" for instructing mathemathics at the

(reiberg G"mnasium , andfrom 18.) at the bergakademie as well#

Weisbach was also known to ha$e written a number of books , of which the

Bergmaschinenmechanik was the first in 1835.in 1839 Weisbach took a trip to the Paris

Industrial !position and depicted a keen interest in h"draulics which led to his first paper in

this field and #imultaneoul" he contributed greatl" to the de$elopment of mine sur$e"ingmethods %introducing the theodolite in place of compass and protractor # &dditionall" he

assumed the resonisbilt" for courses in descriti$e geometr" , cr"stallograh" ,and otics as

well as mechanics #in 18// weisbach attended the aris World *osition , recei$ing and

correcting roof for a new edition of his&echaniken route# Weisbach carrer was incredible , he

ublished fourteen books and fift" 2nine aers on mathematics, mechanics and sur$e"ing ,

but mostl" on h"draulics # weisbach recei$ed a series of rofessional honors in 18/0 ,including

and honorar" doctorate from the ni$ersit" of 3ei4ig in 18/5 and the first honorar"

membershi granted b" the $erein eutscher %ngenieure in 1860#&dditionall" he was a

corresonding member of the St# etersburg &cadem" of Sciences, the Ro"al Swedish &cadem"

of Sciences, and the &ccademia dei 3incei#

Weisbach also contributed significantl" to what is know as the arc"2Weisbach e7uationwhich

in fluid d"namics is an e7uation which relates head loss or ressure due to friction along a

secified length of ie to the a$erage $elocit" of the fluid flow #

+he head loss formula which arc" and Weisbach de$eloed for head loss is calculated b" the

use of the e7uation 1#0 below , where hf is head loss due to friction , 3 is the legth of the ie ,

is the iameter of the ie ,- the a$erage $elocit" , g is acceleration due to gra$it" andf' is the

arc" friction factor

7uation 1#0

+he arc" Weisbach 7uation is also useful to e*ress ead loss in terms of $olumetric flow

rate in Control $olume , with carefull substitution the e7uation 1#) is utili4ed #- is the a$erage

$elocit" of the fluid flow , 9 is the $olumetric flor rate and(w is the wetted cross:sectional area
http://en.wikipedia.org/w/index.php?title=Mittelschmiedeberg&action=edit&redlink=1http://en.wikipedia.org/wiki/Friedrich_Mohshttp://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equationhttp://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equationhttp://en.wikipedia.org/wiki/Friedrich_Mohshttp://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equationhttp://en.wikipedia.org/w/index.php?title=Mittelschmiedeberg&action=edit&redlink=1


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; 7uation 1#)

+he final arc" 2Weisbach e7uation forhead lossin terms of $olumetric flow rateis then

efined , assuming a full flowing ie as e7uation 1#.

Practical applications

%n h"draulic engineeringalications, it is often desirable to e*ress the head loss in terms of

$olumetric flow rate in the ie# (or this, it is necessar" to substitute the following into the

original head loss form of the arc"2Weisbach e7uation

where

)is, as abo$e, the a$erage $elocit" of the fluid flow, e7ual to the $olumetric flow rateer

unit cross:sectional wetted area?

*is the $olumetric flow rate?

(wis the cross:sectional wetted area#

(or the general case of an arbitraril":full ie, the $alue of(wwill not be immediatel" known,

being an imlicit function of ie sloe, cross:sectional shae, flow rate and other $ariables# %f,
http://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_engineeringhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_engineeringhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameter


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howe$er, the ie is assumed to be full flowing and of circular cross:section, as is common in

ractical scenarios, then

where'is thediameterof the ie

Substituting these results into the original formulation "ields the final e7uation for head lossin

terms of $olumetric flow ratein a full:flowing circular ie

where all s"mbols are defined as abo$e#

where

hfis the head loss due to friction ?

3 is the length of the ie ?
http://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Volumetric_flow_rate


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is the h"draulic diameterof the ie ?

)is the a$erage $elocit" of the fluid flow, e7ual to the$olumetric flow rateer unit

cross:sectional wetted area?

gis the local acceleration due togra$it"?

f'is a dimensionless coefficient called the arc" friction factor#Acitation neededB%t can be found

from a !ood" diagramor more recisel" b" sol$ing the!odified Colebrook e7uation#

o not confuse this with the (anning (riction factor, f#

%n fluid d"namics, the DarcyWeisbach equationis ahenomenologicale7uation, which relatesthe head loss orressureloss due to frictionalong a gi$en length of ie to the a$erage

$elocit" of the fluid flow# +he e7uation is named after enr" arc"andJulius Weisbach#

+he arc"2Weisbach e7uation contains a dimensionlessfriction factor, known as the Darcy

friction factor# +his is also called the DarcyWeisbach friction factoror Moody friction

factor# +he arc" friction factor is four times the (anning friction factor, with which it should

not be confused#A1B

Head loss form

ead losscan be calculated with

where


http://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Earth's_gravity#Variations_on_Earthhttp://en.wikipedia.org/wiki/Earth's_gravity#Variations_on_Earthhttp://en.wikipedia.org/wiki/Darcy_friction_factor_formulaehttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Moody_diagramhttp://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Phenomenology_(science)http://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Frictionhttp://en.wikipedia.org/wiki/Henry_Darcyhttp://en.wikipedia.org/wiki/Henry_Darcyhttp://en.wikipedia.org/wiki/Julius_Weisbachhttp://en.wikipedia.org/wiki/Julius_Weisbachhttp://en.wikipedia.org/wiki/Dimension_analysishttp://en.wikipedia.org/wiki/Fanning_friction_factorhttp://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation#cite_note-1http://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Earth's_gravity#Variations_on_Earthhttp://en.wikipedia.org/wiki/Darcy_friction_factor_formulaehttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Moody_diagramhttp://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Phenomenology_(science)http://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Frictionhttp://en.wikipedia.org/wiki/Henry_Darcyhttp://en.wikipedia.org/wiki/Julius_Weisbachhttp://en.wikipedia.org/wiki/Dimension_analysishttp://en.wikipedia.org/wiki/Fanning_friction_factorhttp://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation#cite_note-1http://en.wikipedia.org/wiki/Head_loss


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$olumetric flow rate in the ie# (or this, it is necessar" to substitute the following into theoriginal head loss form of the arc"2Weisbach e7uation

where

)is, as abo$e, the a$erage $elocit" of the fluid flow, e7ual to the $olumetric flow rateerunit cross:sectional wetted area?



(or the general case of an arbitraril":full ie, the $alue of(wwill not be immediatel" known,

being an imlicit function of ie sloe, cross:sectional shae, flow rate and other $ariables# %f,



http://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Earth's_gravity#Variations_on_Earthhttp://en.wikipedia.org/wiki/Earth's_gravity#Variations_on_Earthhttp://en.wikipedia.org/wiki/Darcy_friction_factor_formulaehttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Moody_diagramhttp://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/wiki/Hydraulic_engineeringhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Earth's_gravity#Variations_on_Earthhttp://en.wikipedia.org/wiki/Darcy_friction_factor_formulaehttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Moody_diagramhttp://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/wiki/Hydraulic_engineeringhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Diameter


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%n 18/D Weisbach was offered a osition at the Eurich ol"technikum ? he

chose to remain at (reiberg and the following "ear assumed the further task of teaching machine

design# &lso in 18// he attended the aris World *osition, recei$ing and correcting roof for a

new edition of his&echaniken route# uring his rofessional career Weisbach ublished

fourteen books and fift":nine aers on mathematics, mechanics, and sur$e"ing, but rimaril" on

h"draulics# &n able e*erimenter, he resented most of his results in!perimental+,"draulik

? the" are also summari4ed in the h"draulics section of his-ehrbuch der

Ingenieur+ und &aschinenmechanik


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the eight of nine children born to Christian Gottlieb Weisbach, a mine foreman, and Christina

Rebekka Stehan, Weisbach recei$ed his earl" education at the %"ceum in &nnaberg and the

'ergschule in (reiberg# %n 18)) borrowed funds enabled him to enter the 'ergakademie, where

!ohs ad$ised him to go on to GFttingen# &fter two "ears at the latter uni$ersit", he followed

!ohs in 18)5 to the +echnical ni$ersit" and ni$ersit" of -ienna, where he studied

mathematics, h"sics, and meachanics# Weisbach sent si* months of the following "eartra$eling on foot through ungar", the +irol, 'a$aria, and bohemia# (rom 18.1 to 18./ he

graduall" assumed resonsibilit" for all instruction in mathematics at the (reiberg G"mnasium

and, from 18.), that at the bergakademie as well, desite a low salar" and little recognition# %n

18.) he married !arie Winkler? their son, &lbin, later became rofessor of mineralog" at the

'ergakademie#

+he first of Weisbach;s numerous ublications,Bergmaschinenmechanik, aeared in 18./, and

the following "ear he was romoted to full rofessor of mathematics, mine machiner", and

sur$e"ing# & tri to the aris %ndustrial *osition in 18.5 increased Weisbach;s interest in

h"drulics and led to his first aers in this field# &t the same time he contributed greatl" to thede$eloment of mine sur$e"ing methos, introducing the theodolite in lace of comass and

rotractor# &arentl" an indefatigable worker, he assumed resonsibilit" for courses in

descriti$e geometr", cr"stallograh", and otics, as well as general mechanics#

Julius Ludwig Weisbach was a German mathematician and enginee

Weisbach studied at theBergakademiein(reibergfrom 18)) : 18)6# &fter that, he studied withCarl (riedrich Gaussin GFttingenand with (riedrich !ohsin -ienna#

%n 18.1 he returned to (reibergwhere he worked as mathematics teacher at the localG"mnasium# %n 18.. he became teacher for !athematics and the +heor" of !ountain !achines

at the (reibergBergakademie# %n 18.6 he was romoted to rofessor for alied mathematics,

mechanics, theor" of mountain machines and so:called&arkscheidekunst#
http://en.wikipedia.org/w/index.php?title=Mittelschmiedeberg&action=edit&redlink=1http://en.wikipedia.org/wiki/Mildenauhttp://en.wikipedia.org/wiki/Erzgebirgehttp://en.wikipedia.org/wiki/Freiberg,_Saxonyhttp://en.wikipedia.org/wiki/Engineerhttp://en.wikipedia.org/wiki/Freiberg,_Saxonyhttp://en.wikipedia.org/wiki/Freiberg,_Saxonyhttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/G%C3%B6ttingenhttp://en.wikipedia.org/wiki/Friedrich_Mohshttp://en.wikipedia.org/wiki/Viennahttp://en.wikipedia.org/wiki/Freiberg,_Saxonyhttp://en.wikipedia.org/w/index.php?title=Mittelschmiedeberg&action=edit&redlink=1http://en.wikipedia.org/wiki/Mildenauhttp://en.wikipedia.org/wiki/Erzgebirgehttp://en.wikipedia.org/wiki/Freiberg,_Saxonyhttp://en.wikipedia.org/wiki/Engineerhttp://en.wikipedia.org/wiki/Freiberg,_Saxonyhttp://en.wikipedia.org/wiki/Carl_Friedrich_Gausshttp://en.wikipedia.org/wiki/G%C3%B6ttingenhttp://en.wikipedia.org/wiki/Friedrich_Mohshttp://en.wikipedia.org/wiki/Viennahttp://en.wikipedia.org/wiki/Freiberg,_Saxony


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Weisbach wrote an influential book for mechanical engineering students, called-ehrbuch der

Ingenieur+ und &aschinenmechanik, which has been e*anded and rerinted on numerous

occasions between 18D/ and 186.#

e also refined the arc" e7uation into the still widel" usedarc"2Weisbach e7uation#

%n 1868 he was elected a foreign member of the Ro"al Swedish &cadem" of Sciences#

%n fluid d"namics, the DarcyWeisbach equationis ahenomenologicale7uation, which relatesthe head loss orressureloss due to frictionalong a gi$en length of ie to the a$erage

$elocit" of the fluid flow# +he e7uation is named after enr" arc"andJulius Weisbach#

+he arc"2Weisbach e7uation contains a dimensionlessfriction factor, known as the Darcyfriction factor# +his is also called the DarcyWeisbach friction factoror Moody friction

factor# +he arc" friction factor is four times the (anning friction factor, with which it should

not be confused#A1B
http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equationhttp://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equationhttp://en.wikipedia.org/wiki/Royal_Swedish_Academy_of_Scienceshttp://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Phenomenology_(science)http://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Frictionhttp://en.wikipedia.org/wiki/Henry_Darcyhttp://en.wikipedia.org/wiki/Henry_Darcyhttp://en.wikipedia.org/wiki/Julius_Weisbachhttp://en.wikipedia.org/wiki/Julius_Weisbachhttp://en.wikipedia.org/wiki/Dimension_analysishttp://en.wikipedia.org/wiki/Fanning_friction_factorhttp://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation#cite_note-1http://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equationhttp://en.wikipedia.org/wiki/Royal_Swedish_Academy_of_Scienceshttp://en.wikipedia.org/wiki/Fluid_dynamicshttp://en.wikipedia.org/wiki/Phenomenology_(science)http://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Pressurehttp://en.wikipedia.org/wiki/Frictionhttp://en.wikipedia.org/wiki/Henry_Darcyhttp://en.wikipedia.org/wiki/Julius_Weisbachhttp://en.wikipedia.org/wiki/Dimension_analysishttp://en.wikipedia.org/wiki/Fanning_friction_factorhttp://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation#cite_note-1


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Head loss form

ead losscan be calculated with

where












$olumetric flow rate in the ie# (or this, it is necessar" to substitute the following into theoriginal head loss form of the arc"2Weisbach e7uation

where
http://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Earth's_gravity#Variations_on_Earthhttp://en.wikipedia.org/wiki/Earth's_gravity#Variations_on_Earthhttp://en.wikipedia.org/wiki/Darcy_friction_factor_formulaehttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Moody_diagramhttp://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/wiki/Hydraulic_engineeringhttp://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Earth's_gravity#Variations_on_Earthhttp://en.wikipedia.org/wiki/Darcy_friction_factor_formulaehttp://en.wikipedia.org/wiki/Wikipedia:Citation_neededhttp://en.wikipedia.org/wiki/Moody_diagramhttp://en.wikipedia.org/w/index.php?title=Modified_Colebrook_equation&action=edit&redlink=1http://en.wikipedia.org/wiki/Hydraulic_engineering


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)is, as abo$e, the a$erage $elocit" of the fluid flow, e7ual to the $olumetric flow rateer

unit cross:sectional wetted area?



(or the general case of an arbitraril":full ie, the $alue of(wwill not be immediatel" known,being an imlicit function of ie sloe, cross:sectional shae, flow rate and other $ariables# %f,






http://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Volumetric_flow_ratehttp://en.wikipedia.org/wiki/Hydraulic_diameterhttp://en.wikipedia.org/wiki/Diameterhttp://en.wikipedia.org/wiki/Head_losshttp://en.wikipedia.org/wiki/Volumetric_flow_rate

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Julius Weisbach