Kayan Matsi na Ruwa
A fannin kimiyyar lissafi, ana bayyana matsin lamba a matsayin ƙarfi a kowace yanki, inda alkiblar ƙarfin take daidai da yankin saman. A fannin lissafi, ana bayyana matsin lamba ta hanyar lissafi P = F/A, inda P = matsin lamba, F = ƙarfi da A = yankin saman. Naúrar ƙarfi (F) ita ce Newton (N), naúrar yanki murabba'i ne (m2 ) . Tunda matsin lamba ƙarfi ne a kowace yanki, naúrar matsin lamba shine N/m2 . Wani suna na N/m2 shine pascal (Pascal). Ana amfani da Pascal a matsayin naúrar matsin lamba don girmama Blaise Pascal.
Idan ruwa yana hutawa, yana yin ƙarfi a tsaye ga dukkan saman da yake hulɗa da shi. Misali, yi la'akari da ruwa a cikin gilashi; kowane ɓangare na ruwan yana yin ƙarfi a tsaye ga bangon gilashi. Saboda haka, kowane ɓangare na ruwan yana yin ƙarfi a tsaye ga kowane yanki na akwati da yake zaune. Wannan muhimmin siffa ce ta ruwa mai tsayawa, ruwa a hutawa. Lokacin da ruwa ya yi ƙarfi a kan wani wuri, inda ƙarfin ba ya tsaye, saman zai yi ƙarfin amsawa, kuma ba a tsaye ba. Wannan zai sa ruwan ya gudana. Duk da haka, a zahiri, ruwan yana nan a tsaye. Saboda haka, a cikin ruwa a hutawa, ƙarfin koyaushe yana tsaye ga saman akwatin da yake zaune.
Wani muhimmin siffa ta ruwa a lokacin hutawa ita ce koyaushe yana yin matsin lamba a kowane bangare. Don fahimtar wannan sosai, sanya abu mai iyo a cikin akwati na ruwa. Idan ruwan ya yi tsit gaba ɗaya, abu zai kasance a tsaye saboda matsin lambar da aka yi a samansa duka daidai yake. Idan matsin lambar ruwa bai daidaita ba, za a sami ƙarfin da zai sa abu ya motsa.
Tasirin zurfin kan matsin lamba
Ta yaya zurfin ko tsayi ke shafar matsin ruwa? Shin matsin ruwan teku a zurfin mita 10 yayi daidai da matsin ruwan teku a zurfin mita 100? Bari mu yi la'akari da matsin ruwan da ke cikin akwati kamar yadda aka nuna a cikin hoton. Tsawon ginshiƙin ruwa shine h kuma yankin da ke tsakaninsa shine A. Menene matsin ruwan da ke ƙasan akwatin?
w = nauyin ruwa, h = tsayin ginshiƙin ruwa a cikin akwati mai siffar silinda, A = yankin saman kuma P shine matsin lamba.
Bayani:
w = nauyi
ρ = yawa
m = taro
g = hanzari saboda nauyi
V = hA = girman ginshiƙin ruwa (h = tsayi, A = yankin saman)
Idan muka haɗa shi cikin lissafin matsin lamba, za mu sami:
p = ρ gh → Daidaito 1 (kwantena a rufe)
p = pa + ρ gh → Daidaito 2 (kwandon buɗewa)
Bayani:
pa = Matsi a Yanayi
ρ gh = Matsi na Hydrostatic
A cikin hoton da ke sama, ba a nuna matsin lamba a yanayi ba, amma a zahiri, idan akwati da ke ɗauke da ruwa a buɗe yake, matsin lamba a yanayi shi ma zai yi aiki a saman ruwa, wanda aka mayar da shi ƙasa.
Dangane da lissafin da ke sama, ya bayyana cewa matsin lamba yana daidai da yawan ruwa da zurfinsa (haɓaka nauyi yana nan daram). Yayin da zurfin ruwan ke ƙaruwa, matsin lambar kuma yana ƙaruwa. Ruwa kusan ba za a iya matse shi ba saboda nauyin ruwan da ke sama da shi, don haka yawan ruwan yana nan daram. Idan bambancin tsayi ya yi yawa sosai (misali, a cikin ruwan teku mai zurfi sosai), yawan ruwan ya ɗan bambanta. Duk da haka, idan bambancin tsayi bai yi yawa ba, yawan ruwan yana da iri ɗaya ko kuma bambancin ya yi ƙanƙanta sosai har za a iya yin watsi da shi.
Haka kuma za mu iya amfani da lissafin da ke sama don ƙididdige bambancin matsin lamba a zurfin daban-daban. Ana iya sake rubuta lissafin da ke sama kamar haka:
Matsi a Yanayi
Idan muka nutse a ƙarƙashin ruwa, dukkan jikinmu yana lulluɓe da ruwa. Yayin da muka zurfafa, haka nan ma matsin da muke ji yake ƙaruwa. A gaskiya ma, kowace rana yanayi yana lulluɓe mu, wanda ke ci gaba da matsawa a kan dukkan sassan jikinmu, kamar lokacin da muke ƙarƙashin ruwa. Kamar yadda yake a cikin ruwan teku, ana iya kwatanta saman Duniya da "ƙasa" na sararin samaniya. Idan gaskiya ne cewa yanayi ma yana matsawa a kan dukkan sassan jikinmu a kowane lokaci, me yasa ba ma jin sa, kamar muna ƙasan teku? Kwayoyin jikinmu suna riƙe da matsin lamba na ciki wanda kusan iri ɗaya ne da matsin lamba na waje. Wannan shine dalilin da ya sa ba ma jin tasirin wannan bambancin matsin lamba.
Matsin yanayi na duniya shi ma yana canzawa tare da tsayi. Duk da haka, matsin yanayi ya bambanta kaɗan da na ruwa. Sauyin yawan ruwa yana da ƙanƙanta sosai ga ƙananan bambance-bambance a zurfin, don haka ana ɗauka cewa yawan ruwa iri ɗaya ne. Wannan ya bambanta da yawan sararin samaniyar duniya. Yawan iska a wurare daban-daban ya bambanta sosai, don haka ba za mu iya ƙididdige matsin yanayi ta amfani da lissafin da aka samo a sama ba. Bugu da ƙari, babu wata iyaka bayyananniyar da za a iya auna tsayi daga gare ta. Matsin yanayi kuma ya bambanta da yanayi. Don tantance matsin yanayi, muna ɗaukar ma'auni.
Ma'aunin Matsi
Evangelista Torricelli (1608–1647), ɗalibi a Galileo, ya ƙirƙiro wata hanya ta auna matsin lamba a yanayi a shekara ta 1643 ta amfani da barometer ɗinsa na mercury. Barometer ɗin ya ƙunshi dogon bututun gilashi da aka cika da mercury. An juya bututun gilashi da aka cika da mercury a cikin kwano wanda aka cika da mercury.
Idan aka juye bututun gilashi mai ɗauke da mercury, ƙarshen bututun ba ya cika da mercury, yana ɗauke da tururin mercury ne kawai wanda matsin lamba ya yi ƙanƙanta har ba a yi watsi da shi ba (p2 = 0). A saman mercury a cikin farantin, akwai matsin lamba na yanayi wanda aka karkatar da shi ƙasa (yanayi yana matsawa akan mercury a cikin farantin). Wannan matsin lamba na yanayi yana tallafawa ginshiƙin mercury a cikin bututun gilashi. A cikin hoton, matsin lamba na yanayi ana nuna shi ta hanyar po Ana iya ƙididdige girman matsin lamba na yanayi ta amfani da lissafin:
p o = ρ gh
Dangane da sakamakon aunawa, matsakaicin matsin lamba a matakin teku shine 1,013 x 10 5 N/m2 . Ana amfani da girman matsin lamba a matakin teku don ayyana wani sashi na matsin lamba, wato atm (yanayi). Don haka 1 atm = 1,013 x 10 5 N/m2 = 101,3 kPa (kPa = kilo pascal). Wani sashi na matsin lamba shine sandar (wanda galibi ana amfani da shi a fannin yanayi). 1 sanda = 1,00 x 10 5 N/m2 = 100 kPa.
Ta yaya ake samun ƙimar matsin lamba a sararin samaniya da ke sama?
Ma'aunin yana amfani da ƙa'idar da Torricelli ya nuna a sama. Tsayin ginshiƙin mercury da aka yi amfani da shi shine 76 cm (matsin yanayi zai iya ɗaukar ginshiƙin mercury ne kawai wanda tsayinsa ya kai 76,0 cm kawai), inda zafin mercury da aka yi amfani da shi yake daidai 0. oC kuma girman saurin nauyi shine 9,8 m/s2Yawan sinadarin mercury a wannan yanayin shine 13,6 x 103 kg / m3Matsi a yanayi:
Ma'aunin Matsi
Akwai kayan aiki da yawa da ake amfani da su don auna matsin lamba, gami da ma'aunin bututun buɗewa.
A cikin injin auna bututun da aka buɗe, inda bututun yake da siffar U, bututun ya cika da ruwa kaɗan (mercury ko ruwa). Matsin da aka auna yana da alaƙa da bambancin tsayin ruwa biyu da aka saka a cikin bututun. Ana ƙididdige matsin lambar ta amfani da lissafi:
Gabaɗaya, ba samfurin ρ gh ba ne ake ƙididdigewa amma tsayin ruwa (h) saboda wani lokacin ana nuna matsin lamba a cikin millimeters na mercury (mm hg) ko millimeters na ruwa (mm H 2 O). Wani suna na mm hg shine torr (don tunawa da Evangelista Torricelli).
Bayan na'urorin auna ma'aunin manometer, akwai kuma wasu kayan aunawa, wato na'urorin auna aneroid, na injina da na lantarki, gami da na'urorin auna matsi na taya, da sauransu. Kayan aikin da Torricelli ke amfani da shi don auna matsin lamba a yanayi ana kuma kiransa da na'urar auna matsi ta mercury, inda bututun gilashi ke cike da na'urar auna ma'aunin mercury sannan a juya shi zuwa faranti wanda shi ma ya ƙunshi na'urar auna ma'aunin mercury.
Matsi Mai Kyau, Matsi Mai Ma'auni da Matsi Mai Kyau
Lokacin cika tayoyin abin hawa da iska, yawanci ana amfani da ma'aunin matsin lamba na iska. Wannan yana tabbatar da cewa matsin lamba na taya bai yi ƙasa ba ko kuma ya yi yawa. Lokacin cika tayoyin da iska, kawai ana auna matsin lamba na iska a cikin tayar. Ba a la'akari da matsin lamba na yanayi ba. Ba wai kawai lokacin auna matsin lamba na taya ba, har ma a yawancin sauran ma'aunin matsin lamba, ba a auna matsin lamba na yanayi ba. Wannan matsin lamba da aka auna ana kiransa matsin lamba da aka auna. To, menene bambanci tsakanin wannan da matsin lamba na cikakken?
Matsi cikakke = matsin lamba na yanayi + matsin lamba da aka auna. Don haka don samun matsin lamba cikakke, muna ƙara matsin lamba da aka auna zuwa matsin lamba na yanayi. A wata ma'anar, matsin lamba cikakke = matsin lamba gabaɗaya. A lissafi, ana iya rubuta wannan kamar haka:
p = pa + p ma'auni
Misali, idan matsin lambar tayar da muke aunawa = 100 kPa, to matsin lambar da ya dace shine:
p = pa + p ma'auni
p = 101 kPa + 100 kPa
p = 201 kPa
Matsi mai cikakken ƙarfi = 201 kPa.
Akwai wata kalma: matsin lamba na ma'auni, wanda kuma aka sani da matsin lamba na ma'auni. Matsin lamba na ma'auni shine matsin lamba fiye da matsin yanayi. Misali, yi la'akari da matsin lamba na tayoyin babur. Lokacin da tayar babur ta lalace, matsin lamba da ke cikin tayar yana daidai da matsin yanayi (matsin lamba na yanayi = 1,01 x 105 Pa = 101 kPa). Lokacin da tayar ta cika da iska, matsin lamba na tayar yana ƙaruwa ta halitta. Lokacin da matsin lamba na tayar ya wuce 101 kPa, matsin lamba na ma'auni kuma ana kiransa matsin lamba na ma'auni.
Misalan Tambayoyi Kan Matsi Mai Ruwa
Misali tambaya ta 1:
Jirgin ruwa mai saukar ungulu yana nutsewa zuwa zurfin mita 200. Menene matsin lambar da jirgin ruwan mai saukar ungulu ke fuskanta?
nutsewa? g = 10 m/s2
Tattaunawa
An san cewa:
Zurfin (h) = mita 200
Yawan ruwan teku (ρ) = 1,03 x 103 kg / m3 = 1030 kg/m3 (duba teburin yawan yawa)
Matsi a yanayi (pa) = 1 atm = 1 x 105 N / m2 = 1 x105 (Kg m/s2)/m2 = 1 x105 Kg/ms2
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Matsi
Amsa:
Akwatin a buɗe yake don haka ba a haɗa matsin lamba a cikin lissafin ba.
Misali tambaya ta 2:
Ana cika ma'ajiyar ruwa mai tsawon mita 10 da ruwa. Idan saman ma'ajiyar ruwa ya kasance
a rufe, menene matsin lamba na ruwa a ƙasan akwatin? g = 10 m/s2
Tattaunawa
An san cewa:
Tsawo (h) = mita 10
Yawan ruwa (ρ) = 1,00 x 103 kg / m3 = 1000 kg/m3
Matsi a yanayi (pa) = 1 atm = 1 x 105 N / m2 = 1 x105 (kg m/s2) /m2 = 1 x105 Kg/ms2
Saurin gudu saboda nauyi (g) = 10 m/s2
An tambaya: Matsi
Amsa:
An rufe akwati don haka ba a haɗa matsin lamba a cikin lissafin ba.
Misali tambaya ta 3:
Tsayin ginshiƙin ruwa (dama) = 50 cm, yayin da tsayin ɗayan ginshiƙin ruwa (hagu) = 30 cm. Menene yawan sauran ruwan?
Tattaunawa
An san cewa:
Saurin gudu saboda nauyi (g) = 10 m/s2
Matsayin ruwa (h)1= 50 cm
Yawan ruwa (ρ)1= 1,00 x 103 kg / m3 = 1000 kg/m3
Tsawon ruwa (h)2= 30 cm
Yawan sauran ruwa (ρ)2) =?
pa + ρ 1 gh 1 = pa + ρ 2 gh 2
Matsi na yanayi (Pa) da hanzarin nauyi (g) iri ɗaya ne, don haka suna sokewa.
Misali tambaya ta 4:
A cikin bututun gilashi akwai ruwa mai tsawon santimita 10. Matsin ruwan da ke ƙasan bututun shine 1200 N/m2Idan g = 10 m/s2. Yi watsi da matsin lamba na iska. Menene yawan ruwan?
A. 800 kg/m3
B. 900 kg/m3
C. 1000 kg/m3
D. 1200 kg/m3
E. 1300 kg/m3
Tattaunawa:
An sani :
Ketinggian ruwa (h) = 10 cm = mita 0,1
Matsin ruwa (P) a gindin bututun = 1200 N/m2
Haɓaka Nauyi (g) = 10 m/s2
An tambaya :
Yawan yawa ruwa?
Jawab :
Yawan yawa ruwan shine 1200 kg/m23.
Amsar da ta dace ita ce D.
Misali tambaya ta 5:
Mercury a cikin tasoshin da aka haɗa yana da bambancin saman 3 cm. Yawan mercury = 13,6 gr/cm3Tsawon ruwan da ke cikin bututun da ke hagu shine 10 cm. Menene yawan ruwan?
A. 800 kg/m3
B. 1030 kg/m3
C. 1080 kg/m3
D. 1300 kg/m3
E. 1360 kg/m3
Tattaunawa:
An sani :
Tsawo (h) na Mercury = 3 cm = 0,03 m
Yawan Mercury = 13,6 gr/cm3 = 13600 kg/m3
Tsawon (h) na ruwa = 10 cm = 0,1 m
An tambaya :
Yawan yawa ruwa?
Amsa:
Tsarin yana cikin yanayin daidaiton da ba ya canzawa, don haka matsin lambar ruwa (bututun hagu) = matsin lambar mercury (bututun dama)
Piska + Pruwa =Piska + Pmercury
Matsin iska iri ɗaya ne don haka an cire shi daga lissafin
Ruwa na P = iska ta P
Amsar da ta dace ita ce C.
