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BernoullisLawDerivationDiagram

BernoullisLawDerivationDiagram.png(790 × 370 piksel, fayl həcmi: 9 KB, MIME növü: image/png)

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This is a diagram for one derivation of Bernoulli's Equation. I created this image using MetaPost; in order to produce the raster form, I compiled the source with MetaPost, embedded the resulting file in a pdfLaTeX document, viewed the PDF file with GSview (I tried Acrobat Reader, but its antialiasing was rather poor), and took a screen capture.

The MetaPost source code for this image is provided below (it is licensed under the same licenses as the image) in order to allow easy modification of the image. It's not particularly well-written code (one of my goals in creating it was to learn MetaPost), but anyone who might find it useful can try to make some use of it.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % bernoulli.mp  % % A MetaPost diagram  % % Created on 12 July 2005  % % Copyright (c) 2005 by MannyMax  % % Some rights reserved; see accompanying information for details  % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% beginfig(1); u := 1cm; path t,b,m,pa[],pb[]; pair a[],b[]; picture alab[],blab[]; numeric lwidth,lheight,rwidth,rheight,tubelen,cpgap; color backcol,chunkcol,capcol; lwidth = 1u; rwidth = 2u; lheight= 2u; rheight= 3u; tubelen= 10u; cpgap = 1u; %set diagram colors backcol = 0.27734375*green + 0.73828125*blue; chunkcol= 0.62500000*green + 0.88281250*blue; capcol = 0.70703125*green + 0.90234375*blue; z0=( 0, lheight+(lwidth/2)); z4=((tubelen/2)-cpgap, lheight+(lwidth/2)); z5=((tubelen/2)+cpgap, rheight+(rwidth/2)); z1=( tubelen, rheight+(rwidth/2)); z2=( 0, lheight-(lwidth/2)); z6=((tubelen/2)-cpgap, lheight-(lwidth/2)); z7=((tubelen/2)+cpgap, rheight-(rwidth/2)); z3=( tubelen, rheight-(rwidth/2)); t=z0---z4..z5---z1; b=z2---z6..z7---z3; m=1/2[z0,z2]..1/2[z4,z6]..1/2[z5,z7]..1/2[z1,z3]; fill buildcycle(z0--z2,t,z1--z3,b) withcolor backcol; fill unitsquare xscaled tubelen yscaled 0.25u shifted (0,-0.25u) withcolor 0.75*white; linecap := butt; draw (0,0)--(tubelen,0); linecap := rounded; %DRAW CHUNK A a0=point(0.3) of t; a1=point(0.8) of t; a2=point(0.3) of b; a3=point(0.8) of b; pa1=buildcycle(a0--a2,t,a1--a3,b); pa2 = fullcircle rotated 180 xscaled (0.2*lwidth) yscaled lwidth shifted 1/2[a0,a2]; pa3 = halfcircle rotated -90 xscaled (0.2*lwidth) yscaled lwidth shifted 1/2[a1,a3]; pa4 = halfcircle rotated 90 xscaled (0.2*lwidth) yscaled lwidth shifted 1/2[a1,a3]; pa5 = buildcycle(pa2,t,pa3,b); fill pa2 withcolor capcol; fill pa5 withcolor chunkcol; draw pa2; draw pa3; draw pa4 dashed evenly; a9 = center(buildcycle(pa4,pa3)); pa6 = a9--(a9+(a9-center(pa2))/3); draw pa6 cutafter pa3 withpen pencircle scaled 1; drawarrow pa6 cutbefore pa3 withpen pencircle scaled 1; label.rt (btex $v_1$ etex, point(1) of pa6); pa7 = (a2-(0.2u,0.5u)){dir(90)}..2/5[a2,center(pa2)]; drawarrow pa7; label.bot(btex $A_1$ etex, point(0) of pa7); a4 = whatever[a0,a3]=whatever[a1,a2]; a5 = (xpart(a4),0); a6 = a5+(0,1u); drawdblarrow a5--a4; draw (a4-(0.1u,0))--(a4+(0.1u,0)); alab1 = thelabel(btex $h_1$ etex, (0,0)); unfill bbox alab1 shifted a6; draw alab1 shifted a6; a11 = center(pa2); a10 = a11+(a11-a9)/8; drawarrow a10--a11 withpen pencircle scaled 2; label.lft(btex $p_1$ etex, 1/4[a10,a11]); a7 = a0 + (0,0.35u); a8 = a1 + (0,0.35u); draw a0--(a7 + (0,0.175u)) withcolor 0.5*white; draw a1--(a8 + (0,0.175u)) withcolor 0.5*white; drawdblarrow a7--a8; alab2 =thelabel(btex $v_1\Delta t=s_1$ etex, (0,0)); unfill bbox alab2 shifted 1/2[a7,a8]; draw alab2 shifted 1/2[a7,a8]; %DRAW CHUNK B b0=point(2.2) of t; b1=point(2.6) of t; b2=point(2.2) of b; b3=point(2.6) of b; pb1=buildcycle(b0--b2,t,b1--b3,b); fill pb1 withcolor 0.6[blue,white]; pb2 = fullcircle rotated 180 xscaled (0.2*rwidth) yscaled rwidth shifted 1/2[b0,b2]; pb3 = halfcircle rotated -90 xscaled (0.2*rwidth) yscaled rwidth shifted 1/2[b1,b3]; pb4 = halfcircle rotated 90 xscaled (0.2*rwidth) yscaled rwidth shifted 1/2[b1,b3]; pb5 = buildcycle(pb2,t,pb3,b); fill pb2 withcolor capcol; fill pb5 withcolor chunkcol; draw pb2; draw pb3; draw pb4 dashed evenly; b9 = center(buildcycle(pb4,pb3)); pb6 = b9--(b9+(b9-center(pb2))/3); draw pb6 cutafter pb3 withpen pencircle scaled 1; drawarrow pb6 cutbefore pb3 withpen pencircle scaled 1; label.rt (btex $v_2$ etex, point(1) of pb6); pb7 = (b2-(0.2u,0.5u)){dir(90)}..2/5[b2,center(pb2)]; drawarrow pb7; label.bot(btex $A_2$ etex, point(0) of pb7); b4 = whatever[b0,b3]=whatever[b1,b2]; b5 = (xpart(b4),0); b6 = b5+(0,1u); drawdblarrow b5--b4; draw (b4-(0.1u,0))--(b4+(0.1u,0)); blab1 = thelabel(btex $h_2$ etex, (0,0)); unfill bbox blab1 shifted b6; draw blab1 shifted b6; b11 = center(pb2); b10 = b11+(b11-b9)/8; drawarrow b10--b11 withpen pencircle scaled 2; label.lft(btex $p_2$ etex, 1/4[b10,b11]); b7 = b0 + (0,0.35u); b8 = b1 + (0,0.35u); draw b0--(b7 + (0,0.175u)) withcolor 0.6*white; draw b1--(b8 + (0,0.175u)) withcolor 0.6*white; drawdblarrow b7--b8; blab2 =thelabel(btex $v_2\Delta t=s_2$ etex, (0,0)); unfill bbox blab2 shifted 1/2[b7,b8]; draw blab2 shifted 1/2[b7,b8]; %DRAW FLUID TUBE linecap := butt; draw t withpen pencircle scaled 1; draw b withpen pencircle scaled 1; path acap,bcap,bcapa,bcapb; acap = fullcircle rotated 180 xscaled (0.2*lwidth) yscaled lwidth shifted 1/2[z0,z2]; bcapa = halfcircle rotated -90 xscaled (0.2*rwidth) yscaled rwidth shifted 1/2[z1,z3]; bcapb = halfcircle rotated 90 xscaled (0.2*rwidth) yscaled rwidth shifted 1/2[z1,z3]; bcap = buildcycle(bcapa,bcapb); fill acap withcolor backcol; fill bcap withcolor backcol; linecap := rounded; draw acap withpen pencircle scaled 1; draw bcapa withpen pencircle scaled 1; draw bcapb withpen pencircle scaled 1 dashed evenly; %uncomment the following line to draw a density symbol in the center of the figure %label (btex $\rho$ etex, 1/2[point 1.5 of t, point 1.5 of b]); endfig; 
I, the copyright holder of this work, hereby publish it under the following licenses:
Bu sənədi GNU Azad Sənədləşdirmə Lisenziyası, Versiya 1.2 və ya Azad Proqram Fondu tərəfindən nəşr olunan hər hansı sonrakı versiya şərtlərinə əsasən dəyişməz bölmələr, ön qapaq mətnləri və arxa qapaq mətnləri olmadan köçürmək, yayımlamaq və / və ya dəyişdirmək üçün icazə verilir; Lisenziyanın bir nüsxəsi GNU Azad Sənədləşdirmə Lisenziyası adlı hissəyə daxil edilmişdir.

Bu fayl Creative Commons Attribution-Share Alike 3.0 Sinqapur lisenziyası altında yayımlanır.
Azadsınız:
  • paylaşmaq – əsəri köçürmək, paylamaq və ötürmək üçün
  • remiks etmək – əsəri adaptasiya etmək
Aşağıdakı şərtlərə riayət etməklə:
  • istinad – Müvafiq kredit verməlisiniz, lisenziyaya bir keçid verməlisiniz və dəyişikliklərin olub olmadığını bildirməlisiniz. Bunu hər hansı bir ağlabatan şəkildə edə bilərsiniz, ancaq lisenziyalaşdırıcının sizi və ya istifadənizi təsdiqləməsini təklif edən bir şəkildə deyil.
  • bənzər paylaşma – Əsəri remix edirsinizsə, dəyişdirirsinizsə və ya üzərində iş aparırsınızsa, öz töhfələrinizi orijinalda olduğu kimi eyni və ya uyğun lisenziya altında yayımlamalısınız.
This licensing tag was added to this file as part of the GFDL licensing update.

This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic license.
Azadsınız:
  • paylaşmaq – əsəri köçürmək, paylamaq və ötürmək üçün
  • remiks etmək – əsəri adaptasiya etmək
Aşağıdakı şərtlərə riayət etməklə:
  • istinad – Müvafiq kredit verməlisiniz, lisenziyaya bir keçid verməlisiniz və dəyişikliklərin olub olmadığını bildirməlisiniz. Bunu hər hansı bir ağlabatan şəkildə edə bilərsiniz, ancaq lisenziyalaşdırıcının sizi və ya istifadənizi təsdiqləməsini təklif edən bir şəkildə deyil.
  • bənzər paylaşma – Əsəri remix edirsinizsə, dəyişdirirsinizsə və ya üzərində iş aparırsınızsa, öz töhfələrinizi orijinalda olduğu kimi eyni və ya uyğun lisenziya altında yayımlamalısınız.
İstədiyiniz lisenziyanı seçə bilərsiniz.

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    fayl, bernoullislawderivationdiagram, fayl, faylın, tarixçəsi, fayl, keçidləri, faylın, qlobal, istifadəsidaha, yüksək, versiyası, yoxdur, bernoullislawderivationdiagram, 8206, piksel, fayl, həcmi, mime, növü, image, fayl, vikimedia, commons, dadırvə, digər, l. Fayl Faylin tarixcesi Fayl kecidleri Faylin qlobal istifadesiDaha yuksek versiyasi yoxdur BernoullisLawDerivationDiagram png 8206 790 370 piksel fayl hecmi 9 KB MIME novu image png Bu fayl Vikimedia Commons dadirve diger layihelerde istifade edile biler Faylin tesvir sehifesine get File BernoullisLawDerivationDiagram svg is a vector version of this file It should be used in place of this PNG file when not inferior File BernoullisLawDerivationDiagram png File BernoullisLawDerivationDiagram svg For more information see Help SVG In other languages Alemannisch nbsp العربية nbsp belaruskaya tarashkevica nbsp blgarski nbsp ব ল nbsp catala nbsp nohchijn nbsp cestina nbsp dansk nbsp Deutsch nbsp Ellhnika nbsp English nbsp British English nbsp Esperanto nbsp espanol nbsp eesti nbsp euskara nbsp فارسی nbsp suomi nbsp francais nbsp Frysk nbsp galego nbsp עברית nbsp hrvatski nbsp magyar nbsp հայերեն nbsp Bahasa Indonesia nbsp Ido nbsp italiano nbsp 日本語 nbsp ქართული nbsp 한국어 nbsp lietuviu nbsp makedonski nbsp മലയ ള nbsp Bahasa Melayu nbsp norsk bokmal nbsp Plattduutsch nbsp Nederlands nbsp norsk nynorsk nbsp norsk nbsp occitan nbsp polski nbsp portugues nbsp portugues do Brasil nbsp romană nbsp russkij nbsp sicilianu nbsp Scots nbsp slovencina nbsp slovenscina nbsp srpski srpski nbsp svenska nbsp தம ழ nbsp ithy nbsp Turkce nbsp tatarcha tatarca nbsp ukrayinska nbsp veneto nbsp Tiếng Việt nbsp 中文 简体 nbsp 中文 繁體 nbsp nbsp This is a diagram for one derivation of Bernoulli s Equation I created this image using MetaPost in order to produce the raster form I compiled the source with MetaPost embedded the resulting file in a pdfLaTeX document viewed the PDF file with GSview I tried Acrobat Reader but its antialiasing was rather poor and took a screen capture The MetaPost source code for this image is provided below it is licensed under the same licenses as the image in order to allow easy modification of the image It s not particularly well written code one of my goals in creating it was to learn MetaPost but anyone who might find it useful can try to make some use of it bernoulli mp nbsp A MetaPost diagram nbsp Created on 12 July 2005 nbsp Copyright c 2005 by MannyMax nbsp Some rights reserved see accompanying information for details nbsp beginfig 1 u nbsp 1cm path t b m pa pb pair a b picture alab blab numeric lwidth lheight rwidth rheight tubelen cpgap color backcol chunkcol capcol lwidth 1u rwidth 2u lheight 2u rheight 3u tubelen 10u cpgap 1u set diagram colors backcol 0 27734375 green 0 73828125 blue chunkcol 0 62500000 green 0 88281250 blue capcol 0 70703125 green 0 90234375 blue z0 0 lheight lwidth 2 z4 tubelen 2 cpgap lheight lwidth 2 z5 tubelen 2 cpgap rheight rwidth 2 z1 tubelen rheight rwidth 2 z2 0 lheight lwidth 2 z6 tubelen 2 cpgap lheight lwidth 2 z7 tubelen 2 cpgap rheight rwidth 2 z3 tubelen rheight rwidth 2 t z0 z4 z5 z1 b z2 z6 z7 z3 m 1 2 z0 z2 1 2 z4 z6 1 2 z5 z7 1 2 z1 z3 fill buildcycle z0 z2 t z1 z3 b withcolor backcol fill unitsquare xscaled tubelen yscaled 0 25u shifted 0 0 25u withcolor 0 75 white linecap nbsp butt draw 0 0 tubelen 0 linecap nbsp rounded DRAW CHUNK A a0 point 0 3 of t a1 point 0 8 of t a2 point 0 3 of b a3 point 0 8 of b pa1 buildcycle a0 a2 t a1 a3 b pa2 fullcircle rotated 180 xscaled 0 2 lwidth yscaled lwidth shifted 1 2 a0 a2 pa3 halfcircle rotated 90 xscaled 0 2 lwidth yscaled lwidth shifted 1 2 a1 a3 pa4 halfcircle rotated 90 xscaled 0 2 lwidth yscaled lwidth shifted 1 2 a1 a3 pa5 buildcycle pa2 t pa3 b fill pa2 withcolor capcol fill pa5 withcolor chunkcol draw pa2 draw pa3 draw pa4 dashed evenly a9 center buildcycle pa4 pa3 pa6 a9 a9 a9 center pa2 3 draw pa6 cutafter pa3 withpen pencircle scaled 1 drawarrow pa6 cutbefore pa3 withpen pencircle scaled 1 label rt btex v 1 etex point 1 of pa6 pa7 a2 0 2u 0 5u dir 90 2 5 a2 center pa2 drawarrow pa7 label bot btex A 1 etex point 0 of pa7 a4 whatever a0 a3 whatever a1 a2 a5 xpart a4 0 a6 a5 0 1u drawdblarrow a5 a4 draw a4 0 1u 0 a4 0 1u 0 alab1 thelabel btex h 1 etex 0 0 unfill bbox alab1 shifted a6 draw alab1 shifted a6 a11 center pa2 a10 a11 a11 a9 8 drawarrow a10 a11 withpen pencircle scaled 2 label lft btex p 1 etex 1 4 a10 a11 a7 a0 0 0 35u a8 a1 0 0 35u draw a0 a7 0 0 175u withcolor 0 5 white draw a1 a8 0 0 175u withcolor 0 5 white drawdblarrow a7 a8 alab2 thelabel btex v 1 Delta t s 1 etex 0 0 unfill bbox alab2 shifted 1 2 a7 a8 draw alab2 shifted 1 2 a7 a8 DRAW CHUNK B b0 point 2 2 of t b1 point 2 6 of t b2 point 2 2 of b b3 point 2 6 of b pb1 buildcycle b0 b2 t b1 b3 b fill pb1 withcolor 0 6 blue white pb2 fullcircle rotated 180 xscaled 0 2 rwidth yscaled rwidth shifted 1 2 b0 b2 pb3 halfcircle rotated 90 xscaled 0 2 rwidth yscaled rwidth shifted 1 2 b1 b3 pb4 halfcircle rotated 90 xscaled 0 2 rwidth yscaled rwidth shifted 1 2 b1 b3 pb5 buildcycle pb2 t pb3 b fill pb2 withcolor capcol fill pb5 withcolor chunkcol draw pb2 draw pb3 draw pb4 dashed evenly b9 center buildcycle pb4 pb3 pb6 b9 b9 b9 center pb2 3 draw pb6 cutafter pb3 withpen pencircle scaled 1 drawarrow pb6 cutbefore pb3 withpen pencircle scaled 1 label rt btex v 2 etex point 1 of pb6 pb7 b2 0 2u 0 5u dir 90 2 5 b2 center pb2 drawarrow pb7 label bot btex A 2 etex point 0 of pb7 b4 whatever b0 b3 whatever b1 b2 b5 xpart b4 0 b6 b5 0 1u drawdblarrow b5 b4 draw b4 0 1u 0 b4 0 1u 0 blab1 thelabel btex h 2 etex 0 0 unfill bbox blab1 shifted b6 draw blab1 shifted b6 b11 center pb2 b10 b11 b11 b9 8 drawarrow b10 b11 withpen pencircle scaled 2 label lft btex p 2 etex 1 4 b10 b11 b7 b0 0 0 35u b8 b1 0 0 35u draw b0 b7 0 0 175u withcolor 0 6 white draw b1 b8 0 0 175u withcolor 0 6 white drawdblarrow b7 b8 blab2 thelabel btex v 2 Delta t s 2 etex 0 0 unfill bbox blab2 shifted 1 2 b7 b8 draw blab2 shifted 1 2 b7 b8 DRAW FLUID TUBE linecap nbsp butt draw t withpen pencircle scaled 1 draw b withpen pencircle scaled 1 path acap bcap bcapa bcapb acap fullcircle rotated 180 xscaled 0 2 lwidth yscaled lwidth shifted 1 2 z0 z2 bcapa halfcircle rotated 90 xscaled 0 2 rwidth yscaled rwidth shifted 1 2 z1 z3 bcapb halfcircle rotated 90 xscaled 0 2 rwidth yscaled rwidth shifted 1 2 z1 z3 bcap buildcycle bcapa bcapb fill acap withcolor backcol fill bcap withcolor backcol linecap nbsp rounded draw acap withpen pencircle scaled 1 draw bcapa withpen pencircle scaled 1 draw bcapb withpen pencircle scaled 1 dashed evenly uncomment the following line to draw a density symbol in the center of the figure label btex rho etex 1 2 point 1 5 of t point 1 5 of b endfig I the copyright holder of this work hereby publish it under the following licenses Bu senedi GNU Azad Senedlesdirme Lisenziyasi Versiya 1 2 ve ya Azad Proqram Fondu terefinden nesr olunan her hansi sonraki versiya sertlerine esasen deyismez bolmeler on qapaq metnleri ve arxa qapaq metnleri olmadan kocurmek yayimlamaq ve ve ya deyisdirmek ucun icaze verilir Lisenziyanin bir nusxesi GNU Azad Senedlesdirme Lisenziyasi adli hisseye daxil edilmisdir http www gnu org copyleft fdl html GFDL GNU Free Documentation License true true Bu fayl Creative Commons Attribution Share Alike 3 0 Sinqapur lisenziyasi altinda yayimlanir Azadsiniz paylasmaq eseri kocurmek paylamaq ve oturmek ucun remiks etmek eseri adaptasiya etmek Asagidaki sertlere riayet etmekle istinad Muvafiq kredit vermelisiniz lisenziyaya bir kecid vermelisiniz ve deyisikliklerin olub olmadigini bildirmelisiniz Bunu her hansi bir aglabatan sekilde ede bilersiniz ancaq lisenziyalasdiricinin sizi ve ya istifadenizi tesdiqlemesini teklif eden bir sekilde deyil benzer paylasma Eseri remix edirsinizse deyisdirirsinizse ve ya uzerinde is aparirsinizsa oz tohfelerinizi orijinalda oldugu kimi eyni ve ya uygun lisenziya altinda yayimlamalisiniz This licensing tag was added to this file as part of the GFDL licensing update http creativecommons org licenses by sa 3 0 CC BY SA 3 0 Creative Commons Attribution Share Alike 3 0 true trueThis file is licensed under the Creative Commons Attribution Share Alike 2 5 Generic license Azadsiniz paylasmaq eseri kocurmek paylamaq ve oturmek ucun remiks etmek eseri adaptasiya etmek Asagidaki sertlere riayet etmekle istinad Muvafiq kredit vermelisiniz lisenziyaya bir kecid vermelisiniz ve deyisikliklerin olub olmadigini bildirmelisiniz Bunu her hansi bir aglabatan sekilde ede bilersiniz ancaq lisenziyalasdiricinin sizi ve ya istifadenizi tesdiqlemesini teklif eden bir sekilde deyil benzer paylasma Eseri remix edirsinizse deyisdirirsinizse ve ya uzerinde is aparirsinizsa oz tohfelerinizi orijinalda oldugu kimi eyni ve ya uygun lisenziya altinda yayimlamalisiniz https creativecommons org licenses by sa 2 5 CC BY SA 2 5 Creative Commons Attribution Share Alike 2 5 true trueIstediyiniz lisenziyani sece bilersiniz CaptionsazerbaycancaAdd a one line explanation of what this file representsportuqalPortuguesItems portrayed in this filetesvir edircopyright status nbsp ingiliscopyrighted nbsp ingilislisenziyaCreative Commons Attribution ShareAlike 3 0 Unported nbsp ingilisGNU 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