5 mau laʻana o ke kānāwai o Bernoulli
1 P1 a hiki v1 ʻo ia ke kaomi a me ka wikiwiki o ka ea ma luna o ka ʻēheu, P2 a hiki v2 ʻo ia ke kaomi a me ka wikiwiki o ka ea ma lalo o ka ʻēheu. No ka lele ʻana o kahi mokulele, ʻo nā kūlana...
A.P.1 = P2 a hiki v1 = v2
B.P1 <P2 a hiki v1 > v2
ʻO C. P1 <P2 a hiki v1 < v2
D.P.1 > P2 a hiki v1 > v2
E.P.1 > P2 a hiki v1 < v2
Kūkākūkā:
Ua ʻike ʻia:
P1 = Kaomi ea ma luna o nā ʻēheu
P2 = Kaomi ea ma lalo o nā ʻēheu
v1 = ka wikiwiki o ka ea ma luna o nā ʻēheu
v2 = ka wikiwiki o ka ea ma lalo o nā ʻēheu
Ua nīnau ʻia :
He aha nā kūlana no ka mokulele e hāpai ai a i ʻole ka mokulele e neʻe ai i luna?
Pane :
Ke Kānāwai o Bernoulli a i ʻole i kapa pololei ʻia Ke Kumumanaʻo o Bernoulli ʻōlelo ʻia inā kiʻekiʻe ka wikiwiki o ka wai, haʻahaʻa ke kaomi wai, a ʻo ka hope, inā haʻahaʻa ka wikiwiki o ka wai, kiʻekiʻe ke kaomi wai. ʻO nā wai he mau mea hiki ke kahe. ʻO nā hiʻohiʻona o nā wai he ea a me ka wai.
Inā kiʻekiʻe ka wikiwiki o ka ea, haʻahaʻa ke kaomi o ka ea, i ka ʻaoʻao ʻē aʻe, inā haʻahaʻa ka wikiwiki o ka ea, kiʻekiʻe ke kaomi o ka ea.
Ke ʻoi aku ka wikiwiki o ka ea ma luna o ka ʻēheu ma mua o ka wikiwiki o ka ea ma lalo o ka ʻēheu, ʻoi aku ka liʻiliʻi o ke kaomi ea ma luna o ka ʻēheu ma mua o ke kaomi ea ma lalo o ka ʻēheu. No ka mea, ʻoi aku ka nui o ke kaomi ea ma lalo o ka ʻēheu, ʻoi aku hoʻi ka nui o ka paʻi ʻana o ka ea ma lalo o ka ʻēheu. I ka ʻaoʻao ʻē aʻe, ʻoi aku ka liʻiliʻi o ke kaomi ea ma luna o ka ʻēheu, no laila, ʻoi aku ka liʻiliʻi o ka paʻi ʻana o ka ea ma luna o ka ʻēheu (P = F/A - ʻo ke kiʻekiʻe o ke kaomi, P, ʻoi aku ka nui o ka ikaika, F).
ʻOi aku ka nui o ka ikaika o ka ea ma lalo o ka ʻēheu, ʻoi aku ka liʻiliʻi o ka ikaika o ka ea ma luna o ka ʻēheu, no laila aia kahi ikaika hopena a i ʻole ka ikaika holoʻokoʻa i kuhikuhi ʻia i luna. Hoʻohuli ʻia kēia ikaika holoʻokoʻa i luna e hoʻoulu ai i ka mokulele e hāpai..
Jadi nā kūlana no ka mokulele e lele aku ʻo P1 <P2 a me v1 > v2
ʻO ka pane pololei ʻo B.
2.
Ma ke kiʻi, ua hoʻopili ʻia ka wai e kahi compressor ma ke kaomi o 120 kPa i loko o ka paipu lalo (1) a kahe i luna i ka wikiwiki o 1 m/s.-1 (g = 10 ms-2 a ʻo ka nui o ka wai he 1000 kg.m-3ʻO ke kaomi wai ma ka paipu luna (II) he….
A. 52,5 kPa
B. 67,5 kPa
C. 80,0 kPa
D. 92,5 kPa
E. 107,5 kPa
Pahana
Ua ʻike ʻia:
Ka radius paipu nui (r)1) = 12 kenimika
Ka radius paipu liʻiliʻi (r2) = 6 kenimika
Kaomi wai i loko o nā paipu nui (p1) = 120 kPa = 120.000 Pascals
Ka wikiwiki o ka wai i loko o nā paipu nui (v)1) = 1 ms-1
Ke kiʻekiʻe o ka paipu nui (h)1) = 0 mika
Ke kiʻekiʻe o ka paipu liʻiliʻi (h)2) = 2 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 ms-2
Ka nui o ka wai (ρ) = 1000 kg.m-3
Ua nīnau ʻia: Kaomi wai i loko o ka paipu 2 (p2)
Pane:
Ua helu ʻia ka wikiwiki o ka wai ma ka paipu 2 me ka hoʻohana ʻana i ka Continuity Equation:
A1 v1 =A2 v2
(π r12)(ʻoiaʻiʻo1) = (π r22)(ʻoiaʻiʻo2)
(r12)(ʻoiaʻiʻo1) = (r22)(ʻoiaʻiʻo2)
(122)(1 m/s) = (62)(ʻoiaʻiʻo2)
144 = 36 v2
v2 = 144/36
v2 = 4m/s
Ua helu ʻia ke kaomi wai ma ka paipu 2 me ka hoʻohana ʻana i ka hoʻohālikelike Bernoulli:
120.000 + ½ (1000)(12) + (1000)(10)(0) = p2 + ½ (1000)(42) + (1000)(10)(2)
120.000 + ½ (1000)(1) + (1000)(10)(0) = p2 + ½ (1000)(16) + (1000)(10)(2)
120.000 + 500 + 0 = p2 + (500)(16) + 20.000
120.000 + 500 = p2 + 8000 + 20.000
120.500 = p2 + 28.000
p2 = 120.500 - 28.000
p2 = 92.500 Pascals
p2 = 92,5 kPa
ʻO D ka pane pololei.
3. E nānā i ke kiʻi ma lalo nei!
Aia ke kiʻekiʻe o ka paipu nui ma luna o ka honua he 5 m a ʻo ke kiʻekiʻe o ka paipu liʻiliʻi he 1 m ma luna o ka honua. ʻO ka nui o ke kahe ʻana o ka wai i loko o ka paipu nui he 36 km/h.-1 me ke kaomi o 9,1 x 105 Pa, ʻoiai ke kaomi i loko o ka paipu liʻiliʻi he 2.105 Pa, a laila ʻo ka wikiwiki o ka wai i loko o ka paipu liʻiliʻi he…. (ka nui o ka wai = 103 kg.m-3)
A. 10 ms-1
B. 20 ms-1
C. 30 ms-1
D. 40 ms-1
E. 50 ms-1
Pahana
Ua ʻike ʻia:
Kaomi wai i loko o nā paipu nui (p1) = 9,1 x 105 Pascal = 910.000 Pascals
Kaomi wai i loko o nā paipu liʻiliʻi (p2) = 2 x 105 Pascal = 200.000 Pascals
Ka wikiwiki o ka wai i loko o nā paipu nui (v)1) = 36 km/h = 36(1000)/(3600) = 36000/3600 =10 m/s
Ke kiʻekiʻe o ka paipu nui (h)1) = -4 mika
Ke kiʻekiʻe o ka paipu liʻiliʻi (h)2) = 0 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 ms-2
Ka nui o ka wai (ρ) = 1000 kg.m-3
Ua nīnau ʻia: Ka wikiwiki o ka wai i loko o ka paipu liʻiliʻi (v)2)
Pane:
Ka wikiwiki o ka wai i loko o ka paipu liʻiliʻi (v)2) ua helu ʻia me ka hoʻohana ʻana i ka hoʻohālikelike Bernoulli:
910.000 + ½ (1000)(102) + (1000)(10)(0) = 200.000 + ½ (1000)(v22) + (1000)(10)(-4)
910.000 + 50.000 + 0 = 200.000 + 500 v22 - 40.000
960.000 = 160.000 + 500 v22
800.000 = 500 v22
800.000 / 500 = v22
1600 = v22
v2 = √1600
v2 = 40m/s
ʻO D ka pane pololei.
4. Ma ke kiʻi, ua hoʻopili ʻia ka wai e kahi compressor ma ke kaomi o 120 kPa i loko o ka paipu lalo (1) a kahe i luna i ka wikiwiki o 1 m/s.-1 (g = 10 ms-2 a ʻo ka nui o ka wai he 1000 kg.m-3ʻO ke kaomi wai ma ka paipu luna (II) he….
A. 52,5 kPa
B. 67,5 kPa
C. 80,0 kPa
D. 92,5 kPa
E. 107,5 kPa
Pahana
Ua ʻike ʻia:
Ka radius paipu nui (r)1) = 12 kenimika
Ka radius paipu liʻiliʻi (r2) = 6 kenimika
Kaomi wai i loko o nā paipu nui (p1) = 120 kPa = 120.000 Pascals
Ka wikiwiki o ka wai i loko o nā paipu nui (v)1) = 1 ms-1
Ke kiʻekiʻe o ka paipu nui (h)1) = 0 mika
Ke kiʻekiʻe o ka paipu liʻiliʻi (h)2) = 2 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 ms-2
Ka nui o ka wai (ρ) = 1000 kg.m-3
Ua nīnau ʻia: Kaomi wai i loko o ka paipu 2 (p2)
Pane:
Ua helu ʻia ka wikiwiki o ka wai ma ka paipu 2 me ka hoʻohana ʻana i ka Continuity Equation:
A1 v1 =A2 v2
(π r12)(ʻoiaʻiʻo1) = (π r22)(ʻoiaʻiʻo2)
(r12)(ʻoiaʻiʻo1) = (r22)(ʻoiaʻiʻo2)
(122)(1 m/s) = (62)(ʻoiaʻiʻo2)
144 = 36 v2
v2 = 144/36
v2 = 4m/s
Ua helu ʻia ke kaomi wai ma ka paipu 2 me ka hoʻohana ʻana i ka hoʻohālikelike Bernoulli:
120.000 + ½ (1000)(12) + (1000)(10)(0) = p2 + ½ (1000)(42) + (1000)(10)(2)
120.000 + ½ (1000)(1) + (1000)(10)(0) = p2 + ½ (1000)(16) + (1000)(10)(2)
120.000 + 500 + 0 = p2 + (500)(16) + 20.000
120.000 + 500 = p2 + 8000 + 20.000
120.500 = p2 + 28.000
p2 = 120.500 - 28.000
p2 = 92.500 Pascals
p2 = 92,5 kPa
ʻO D ka pane pololei.
5. E nānā i ke kiʻi ma lalo nei! ʻO ke kūlana o ka paipu nui he 5 m ma luna o ka honua a ʻo ka paipu liʻiliʻi he 1 m ma luna o ka honua. ʻO ka wikiwiki o ke kahe ʻana o ka wai i loko o ka paipu nui he 36 km/h.-1 me ke kaomi o 9,1 x 105 Pa, ʻoiai ke kaomi i loko o ka paipu liʻiliʻi he 2.105 Pa, a laila ʻo ka wikiwiki o ka wai i loko o ka paipu liʻiliʻi he…. (ka nui o ka wai = 103 kg.m-3)
A. 10 ms-1
B. 20 ms-1
C. 30 ms-1
D. 40 ms-1
E. 50 ms-1
Pahana
Ua ʻike ʻia:
Kaomi wai i loko o nā paipu nui (p1) = 9,1 x 105 Pascal = 910.000 Pascals
Kaomi wai i loko o nā paipu liʻiliʻi (p2) = 2 x 105 Pascal = 200.000 Pascals
Ka wikiwiki o ka wai i loko o nā paipu nui (v)1) = 36 km/h = 36(1000)/(3600) = 36000/3600 =10 m/s
Ke kiʻekiʻe o ka paipu nui (h)1) = -4 mika
Ke kiʻekiʻe o ka paipu liʻiliʻi (h)2) = 0 mika
Ka wikiwiki ma muli o ke koʻikoʻi (g) = 10 ms-2
Ka nui o ka wai (ρ) = 1000 kg.m-3
Ua nīnau ʻia: Ka wikiwiki o ka wai i loko o ka paipu liʻiliʻi (v)2)
Pane:
Ka wikiwiki o ka wai i loko o ka paipu liʻiliʻi (v)2) ua helu ʻia me ka hoʻohana ʻana i ka hoʻohālikelike Bernoulli:
910.000 + ½ (1000)(102) + (1000)(10)(0) = 200.000 + ½ (1000)(v22) + (1000)(10)(-4)
910.000 + 50.000 + 0 = 200.000 + 500 v22 - 40.000
960.000 = 160.000 + 500 v22
800.000 = 500 v22
800.000 / 500 = v22
1600 = v22
v2 = √1600
v2 = 40m/s
ʻO D ka pane pololei.
Puna nīnau:
Nā Nīnau Hoʻokolohua Lahui no ke Kino no ke Kula Kiʻekiʻe/Kula Kiʻekiʻe ʻOihana
