Qaaciddada Bernoulli: Mabaadi'da iyo Adeegsiga
Mabda'a Bernoulli waa fikrad aasaasi ah oo ku saabsan farsamada dareeraha, oo uu ogaaday Daniel Bernoulli, oo ahaa saynisyahan u dhashay Switzerland, qarnigii 18aad. Mabda'ani wuxuu sharxayaa xiriirka ka dhexeeya xawaaraha socodka dareeraha iyo cadaadiska ku jira socodkaas. Maqaalkani wuxuu si qoto dheer uga hadli doonaa qaacidada Bernoulli, fikradaha aasaasiga ah, soo-saarista xisaabta, tusaalooyinka xisaabinta, iyo adeegsigeeda nolol maalmeedka.
Fahmidda Qaaciddada Bernoulli
Qaaciddada Bernoulli waxay sheegaysaa in socodka dareeraha ee ku habboon (iyada oo aan lahayn is jiidjiid), xaddiga tamarta farsamada (tamarta suurtagalka ah, tamarta dhaqdhaqaaqa, iyo cadaadiska) mugga cutub kasta uu yahay mid joogto ah inta uu socdo socodka. Qaaciddadan waxaa lagu sheegay sidan:
\[ P + \frac{1}{2} \rho v^2 + \rho gh = \text{constant} \]
Halkee:
– \( P \) waa cadaadiska dareeraha (Pascals, Pa),
– \( \rho \) waa cufnaanta dareeraha (kiiloogaraamkiiba mitirkiiba saddex jibbaaran, kg/m³),
– \( v \) waa xawaaraha socodka dareeraha (mitirkiiba ilbiriqsi, m/s),
– \( g \) waa dardargelinta cufisjiidadka awgeed (mitirkiiba ilbiriqsigiiba labajibbaaran, m/s²),
– \( h \) waa dhererka dareeraha ka sarreeya tixraaca (mitir ahaan, m).
Mabda'a Bernoulli
Mabda'a Bernoulli wuxuu ku salaysan yahay sharciga ilaalinta tamarta. Socodka dareeraha, tamarta guud ee nidaamka waa inay ahaataa mid joogto ah haddii aan tamar lagu darin ama laga saarin nidaamka. Tamarta guud ee mugga halbeeg kasta waxay ka kooban tahay:
1. Tamarta Cadaadiska (\( P \)): Tamarta ay keento cadaadiska dareeraha.
2. Tamarta Kinetic (\( \frac{1}{2} \rho v^2 \)): Tamar ay keento dhaqdhaqaaqa dareeraha.
3. Tamarta Awoodda Cufisjiidadka (\( \rho gh \)): Tamarta ay keento booska dareere ku jira goobta cufisjiidadka.
Soo saarista Xisaabta ee Qaacidda Bernoulli
Si loo fahmo soo saarista Qaacidda Bernoulli, waxaan tixgelineynaa walax yar oo dareere ah oo ku socota socodka xawaaraha leh \( v \) laga bilaabo barta 1 ilaa barta 2. Haddii aan u maleyno inaysan jirin wax tamar ah oo ka lumaya isjiidjiid ama kulayl, tamarta guud ee dhibcaha 1 iyo 2 waa inay isku mid noqotaa.
Tamarta guud ee ku jirta qodobka 1 (\( E_1 \)) waa:
\[ E_1 = P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 \]
Tamarta guud ee ku jirta qodobka 2 (\( E_2 \)) waa:
\[ E_2 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2 \]
Maadaama tamarta guud ay tahay inay joogto noqoto:
\[ P_1 + \frac{1}{2} \rho v_1^2 + \rho gh_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho gh_2 \]
Kani waa waxa loogu yeero Qaacidda Bernoulli.
Xisaabinta Tusaale ah Iyada oo la adeegsanayo Qaacidda Bernoulli
Ka soo qaad inaan haysanno tuubo jiif ah oo biyuhu ka socdaan barta A ilaa barta B. Barta A, xawaaraha biyuhu waa 2 m/s cadaadiskuna waa 150,000 Pa. Barta B, xawaaraha biyuhu waa 4 m/s. Cufnaanta biyuhu waa 1000 kg/m³. Xisaabi cadaadiska barta B.
Isticmaal Qaacidada Bernoulli:
\[ P_A + \frac{1}{2} \rho v_A^2 + \rho gh_A = P_B + \frac{1}{2} \rho v_B^2 + \rho gh_B \]
Maadaama tuubooyinku ay jiifaan, \( h_A = h_B \), markaa \( \rho gh \) labada meeloodba waa la dayaci karaa:
\[ P_A + \frac{1}{2} \rho v_A^2 = P_B + \frac{1}{2} \rho v_B^2 \]
Ku beddel qiimayaasha la yaqaan:
\[ 150,000 + \frac{1}{2} \jeer 1000 \jeer (2)^2 = P_B + \frac{1}{2} \jeer 1000 \jeer (4)^2 \]
Xisaabi tamarta dhaqdhaqaaqa labada dhinacba:
\[ 150,000 + 2000 = P_B + 8000 \]
\[ 152,000 = P_B + 8000 \]
\[ P_B = 152,000 – 8000 \]
\[ P_B = 144,000 \, \qoraal{Pa} \]
Markaa, cadaadiska barta B waa 144,000 Pa.
Adeegsiga Mabda'a Bernoulli
1. Diyaaradaha: Mabda'a Bernoulli waxaa loo isticmaalaa naqshadeynta baalasha diyaaradaha. Qaabka baalka diyaaradda waxaa loo qaabeeyey si xawaaraha hawada ee ka sarreeya baalka uu uga weynaado kan ka hooseeya baalka. Tani waxay keentaa cadaadis hoose oo ka sarreeya baalka iyo cadaadis sare oo ka hooseeya baalka, taasoo abuurta wiish u oggolaanaya diyaaradda inay duusho.
2. Gawaarida Tartan: Naqshadeynta hawada sare ee gawaarida tartanka waxay isticmaashaa Mabda'a Bernoulli si loo kordhiyo xawaaraha iyo xasilloonida. Qaswadayaasha iyo kala-baxayaasha waxaa loo isticmaalaa in lagu xakameeyo socodka hawada, taasoo kordhinaysa xoogga hoos u dhaca, taas oo hagaajinaysa jiidista gaariga ee wadada.
3. Socodka Dhiigga ee Jirka: Mabda'a Bernoulli wuxuu sidoo kale khuseeyaa socodka dhiigga ee xididdada dhiigga. Kala duwanaanshaha xawaaraha socodka dhiigga iyo cadaadiska qaybaha kala duwan ee jirka ayaa la baran karaa si loo ogaado xaaladaha caafimaad.
4. Mitirka Venturi: Qalab loo isticmaalo in lagu cabbiro heerka socodka dareeraha ee ku jira tuubo. Mitirka Venturi wuxuu leeyahay qayb cidhiidhi ah, taasoo keenta koror ku yimaada xawaaraha socodka dareeraha iyo hoos u dhaca cadaadiska iyadoo la raacayo Mabda'a Bernoulli. Farqiga cadaadiska ee u dhexeeya qaybaha ballaaran iyo kuwa cidhiidhiga ah ayaa loo isticmaalaa in lagu xisaabiyo heerka socodka.
5. Buufinta Cadarka: Buufinta cadarka ama buufinta dareeraha ah waxay isticmaalaan mabda'a Bernoulli. Marka hawada lagu afuufo tuubo cidhiidhi ah, cadaadiska hawada ee ku wareegsan dhammaadka tuubada ayaa hoos u dhaca, taasoo dareeraha cadarka kor u soo jiidaysa tuubada oo ku buufinaysa sidii ceeryaamo fiican.
Arrimaha Saameynaya Adeegsiga Mabda'a Bernoulli
1. Khilaaf: Dhab ahaantii, dareerayaashu ma aha kuwo ku habboon waxaana had iyo jeer jira khilaaf gudaha ah (jilicsanaan) oo sababa luminta tamarta. Tani waxay ka dhigaysaa adeegsiga Mabda'a Bernoulli mid aad u adag.
2. Isku-buufinta Dareeraha: Mabda'a Bernoulli way fududahay in lagu dabaqo dareerayaasha aan la cadaadin karin (sida biyaha). Gaasaska ama dareerayaasha la cadaadin karo, waa in la hagaajiyaa isla'egta.
3. Walaac: Mabda'a Bernoulli wuxuu khuseeyaa socodka caadiga ah ee laminar. Socodka qalalaasaha (aan caadiga ahayn), falanqayntu waxay noqotaa mid aad u adag.
Daraasad Kiis: Isticmaalka Mabda'a Bernoulli ee Naqshadeynta Baalasha Diyaaradaha
Naqshadeynta baalasha diyaaradda waa tusaale caadi ah oo ka mid ah Mabda'a Bernoulli ee ficilka ku jirta. Qaabka sare ee qaloocan iyo kan hoose ee siman ee baalku wuxuu u oggolaanayaa hawada inay si dhakhso leh uga dul marto baalka marka loo eego kan hoos yimaada. Sida laga soo xigtay Mabda'a Bernoulli, xawaaraha hawada ee sare ee baalka ayaa soo saara cadaadis ka hooseeya kan hoos yimaada baalka. Farqiga cadaadiskan wuxuu abuuraa xoogga kor u qaadista ee u oggolaanaya diyaaradda inay duusho.
Ka soo qaad diyaaraddu waxay leedahay baal baalal ah oo ah 25 m². Xawaaraha hawada ee ka sarreeya baalka waa 70 m/s, halka baalka ka hooseeya uu yahay 50 m/s. Cufnaanta hawada waa 1.225 kg/m³. Xisaabi kor u qaadista ka dhalatay.
1. Xisaabi farqiga cadaadiska (\( \Delta P \)) adoo isticmaalaya Qaacidda Bernoulli:
\[ P_{hoose} – P_{top} = \frac{1}{2} \rho (v_{top}^2 – v_{bottom}^2) \]
Ku beddel qiimayaasha la yaqaan:
\[ \Delta P = \frac{1}{2} \times 1.225 \times (70^2 – 50^2) \]
\[ \Delta P = \frac{1}{2} \times 1.225 \times (4900 - 2500) \]
\[ \Delta P = \frac{1}{2} \times 1.225 \times 2400 \]
\[ \Delta P = 1.225 \jeer 1200 \]
\[ \Delta P = 1470 \, \qoraalka{Pa} \]
2. Xisaabi xoogga kor u qaadista (\( F_{lift} \)):
\[ F_{lift} = \Delta P \times A \]
\[ F_{lift} = 1470 \, \qoraalka{Pa} \times 25 \, \qoraalka{m}^2 \]
\[ F_{lift} = 36,750 \, \qoraal{
N} \]
Markaa, awoodda qaadista ee ka dhalata waa 36,750 newtons.
Gabagabo
Mabda'a Bernoulli waa mid ka mid ah aasaaska farsamooyinka dareeraha, isagoo sharraxaya xiriirka ka dhexeeya xawaaraha socodka dareeraha iyo cadaadiska. Markaan fahamno oo aan adeegsanno Qaacidda Bernoulli, waxaan falanqeyn karnaa oo aan naqshadeyn karnaa nidaamyo kala duwan oo ku lug leh socodka dareeraha, laga bilaabo diyaaradaha ilaa mitirrada socodka. In kasta oo ficil ahaan aan inta badan u baahannahay inaan tixgelinno arrimo ay ka mid yihiin is-jiidjiid iyo jahwareer, Mabda'a Bernoulli wuxuu weli yahay qalab lagama maarmaan u ah fahamka dhaqdhaqaaqa dareeraha iyo naqshadeynta xalal injineernimo oo hufan.
