This document discusses fluid mechanics and introduces some key concepts. It states that matter exists in three states - solid, liquid, and gas - which are affected differently by external forces. Liquids and gases can flow or change shape depending on their container, whereas solids maintain their shape. The document then introduces the concept of the ideal fluid and the equation of continuity, which states that the quantity of fluid passing through different sections of a pipe is constant over time. It provides an example of using this equation to calculate the flow rate of water through a pipe.

1. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
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‫ﻣﯿﻜﺎﻧﯿﻜﺎ‬‫اﻟﻤﻮاﺋﻊ‬FLUID MECHANICS
‫ﺗوﺟد‬‫اﻟﻣﺎدة‬‫ﻓﻲ‬‫ﺛﻼث‬‫ﺣﺎﻻت‬‫ھﻲ‬‫اﻟﺣﺎﻟﺔ‬‫اﻟﺻﻠﺑﺔ‬‫واﻟﺣﺎﻟﺔ‬‫اﻟﺳﺎﺋﻠﺔ‬‫واﻟﺣﺎﻟﺔ‬‫اﻟﻐﺎزﯾﺔ‬
‫وﺗﺗﺄﺛر‬‫اﻟﺣﺎﻻت‬‫اﻟﺛﻼث‬‫ﺑﺎﻟﻘوى‬‫اﻟﻣؤﺛرة‬‫ﻋﻠﯾﮭﺎ‬‫ﺑﺻور‬‫ﻣﺧﺗﻠﻔﺔ‬‫ﻓﻔﻲ‬‫ﺣﯾن‬‫أن‬‫اﻟﻣواد‬
‫اﻟﺻﻠﺑﺔ‬‫ﺗﺣﺎﻓظ‬‫ﻋﻠﻰ‬‫ﺷﻛﻠﮭﺎ‬‫ﻓﺈن‬‫اﻟﻣواد‬‫اﻟﺳﺎﺋﻠﺔ‬‫ﺗﺄﺧذ‬ً‫ﺎ‬‫داﺋﻣ‬‫ﺷﻛل‬‫اﻟوﻋﺎء‬‫اﻟذي‬‫ﺗﺣﺗوﯾﮫ‬‫ﻣﻊ‬
‫اﻟﻣﺣﺎﻓظﺔ‬‫ﻋﻠﻰ‬‫اﻟﺣﺟم‬‫أﻣﺎ‬‫اﻟﻣواد‬‫اﻟﻐﺎزﯾﺔ‬‫ﻓﺈﻧﮭﺎ‬‫ﺗﺄﺧذ‬‫ﺷﻛل‬‫اﻟوﻋﺎء‬‫اﻟذي‬‫ﯾﺣﺗوﯾﮭﺎ‬
‫وﺗﻧﺗﺷر‬‫ﻓﯾﮫ‬‫ﻟﺗﻣﻠؤه‬‫وھذا‬‫ﯾﻌﻧﻲ‬‫أن‬‫اﻟﻣواد‬‫اﻟﻐﺎزﯾﺔ‬‫ﻻ‬‫ﺗﺣﺎﻓظ‬‫ﻋﻠﻰ‬‫ﺷﻛﻠﮭﺎ‬‫أو‬‫ﺣﺟﻣﮭﺎ‬.
‫وﺣﺎﻟﺔ‬‫ﻛل‬‫ﻣن‬‫اﻟﻣواد‬‫اﻟﺳﺎﺋﻠﺔ‬‫واﻟﻣواد‬‫اﻟﻐﺎزﯾﺔ‬‫ﻗﺎﺑﻼن‬ ‫ﻷﻧﮭﺎ‬ ‫ﺑﺎﻟﻣواﺋﻊ‬ ‫ﺗﻌرف‬
‫ﻟﻠﺣرﻛﺔ‬)‫اﻟﺗدﻓﻖ‬Flow(‫ﺗﺣت‬‫ﺗﺄﺛﯾر‬‫ﻗوة‬‫ﺧﺎرﺟﯾﺔ‬.
‫دراﺳﺔ‬‫ﻣﯾﻛﺎﻧﯾﻛﺎ‬‫اﻟﻣواﺋﻊ‬‫ﻣن‬‫اﻟﻣواﺿﯾﻊ‬‫اﻟﻣﮭﻣﺔ‬‫ﻓﻲ‬‫اﻟﻔﯾزﯾﺎء‬‫وﺗدﺧل‬‫ﻓﻲ‬‫اﻟﻌدﯾد‬‫ﻣن‬
‫اﻟﻣﺟﺎﻻت‬‫اﻟﻌﻣﻠﯾﺔ‬‫ﻣﺛل‬‫ھﻧدﺳﺔ‬‫اﻟطﯾران‬‫وﺑﻧﺎء‬‫اﻟﺳدود‬‫واﻟﺟﺳور‬‫وطرق‬‫اﻟري‬‫واﻟﻛﺛﯾر‬
‫ﻣن‬‫اﻟﻌﻠوم‬‫اﻟﺗطﺑﯾﻘﯾﺔ‬.
‫ﺳﯾﺗم‬‫ﻣﻌﺎﻟﺟﺔ‬‫ﻣﯾﻛﺎﻧﯾﻛﺎ‬‫اﻟﻣواﺋﻊ‬‫ﺑﺎﺳﺗﺧدام‬‫ﻗواﻧﯾن‬‫ﻧﯾوﺗن‬‫ﻟﻠﺣرﻛﺔ‬‫وﻧظرﯾﺔ‬‫اﻟﺷﻐل‬‫و‬
،‫اﻟطﺎﻗﺔ‬‫وﺳوف‬‫ﻧﺗﻌرض‬‫إﻟﻰ‬‫ﻛﻣﯾﺎت‬‫ﻓﯾزﯾﺎﺋﯾﺔ‬‫ﺟدﯾدة‬‫ﻣﺛل‬‫اﻟﺿﻐط‬‫واﻟﻛﺛﺎﻓﺔ‬.
‫اﻟﻤﺜﺎﻟﻲ‬ ‫اﻟﻤﺎﺋﻊ‬Idea fluid:‫و‬ ‫ﻟﻼﻧﻀﻐﺎط‬ ‫ﻗﺎﺑﻞ‬ ‫ﻏﯿﺮ‬ ‫و‬ ‫ﻏﯿﺮﻟﺰج‬ ‫و‬ ‫ﻣﻨﺘﻈﻢ‬ ‫ﻣﺎﺋﻊ‬ ‫ھﻮ‬
‫دوراﻧﻲ‬ ‫ﻏﯿﺮ‬.
‫اﻻﺳﺗﻣرارﯾﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬The Equation of continuity
‫ﻣوﺿﺢ‬ ‫ھو‬ ‫ﻛﻣﺎ‬ ‫اﻟﻣﻘﺎطﻊ‬ ‫ﻣﺧﺗﻠﻔﺔ‬ ‫أﻧﺑوﺑﺔ‬ ‫ﺧﻼل‬ ‫ﯾﻧﺳﺎب‬ ً‫ﺎ‬‫ﻣﺛﺎﻟﯾ‬ ً‫ﺎ‬‫ﻣﺎﺋﻌ‬ ‫أن‬ ‫ﻧﻔرض‬
‫ﺑﺎﻟﺷﻛل‬.
x1 v1 t
Hence the mass in the portion x1 of the pipe is m1   A1 x1 . On the
other end of the pipe the mass of the fluid moves in time t is
mA2 v2 t.
The mass is conserved m1 m2
A1 v1  A2 v2 This called the equation of continuity
In this case density of the fluid is constant i.e. 
A1 v1 = A2 v2= constant

2. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
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ِ ‫اﻟﺧروج‬ ‫و‬ ‫اﻟدﺧول‬ ‫ﻓﻲ‬ ‫ﺛﺎﺑﺗﺔ‬ ‫اﻟﻣﻧﺳﺎﺑﺔ‬ ‫اﻟﻛﻣﯾﺔ‬A1ⱱ1 = A2ⱱ2 = constant
‫اﻟﻣﺳﺎﺣﺔ‬ ‫ﺿرب‬ ‫ﺣﺎﺻل‬ ‫ﯾﻛون‬ ‫اﻻﺳﺗﻣرارﯾﺔ‬ ‫ﻣﻌﺎدﻟﺔ‬A‫اﻟﺳرﻋﺔ‬ ‫ﻓﻲ‬ⱱ‫ﯾﻛون‬
‫اﻧﺳﯾﺎب‬ ‫أﻧﺑوﺑﺔ‬ ‫ﻷي‬ ‫ﺛﺎﺑت‬Q = Aⱱ)Q‫اﻻﻧﺑوﺑﺔ‬ ‫ﺧﻼل‬ ‫اﻟﻣﺎﺋﻊ‬ ‫اﻻﻧﺳﯾﺎب‬ ‫ﻣﻌدل‬(
‫اﻟﻣﻧﺳﺎﺑﺔ‬ ‫اﻟﻣﺎﺋﻊ‬ ‫ﻛﻣﯾﺔ‬ ‫ﺑﺄﻧﮫ‬ ‫ﯾﻌرف‬ ‫و‬ⱱ‫ﻗدره‬ ‫زﻣن‬ ‫ﺧﻼل‬t
‫أﻧﮫ‬ ‫أن‬Q = ⱱ/t
‫ﻣﺛﺎل‬:‫ﯾﺗم‬‫اﺳﺗﺧدام‬‫أﻧﺎﺑﯾب‬‫اﻟﻣﯾﺎه‬‫ﻧﺻف‬‫ﻗطرھﺎ‬3cm‫ﻟﻣلء‬‫دﻟو‬40‫ﻟﺗر‬.‫إذا‬‫ﻛﺎن‬
‫ﯾﺄﺧذ‬5‫دﻗﺎﺋﻖ‬‫ﻟﻣلء‬،‫دﻟو‬‫ﻣﺎ‬‫ھﻲ‬‫اﻟ‬‫ﺳرﻋﺔ‬)ⱱ(‫ﻣن‬ ‫اﻟﻣﯾﺎه‬ ‫ﺧروج‬‫اﻷﻧﺑوب؟‬
‫اﻟﺣـــل‬:

3. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
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‫ﻣﻼﺣظﺎت‬:‫و‬ ‫اﻟرﺋﯾﺳﯾﺔ‬ ‫اﻟﺷراﯾﯾن‬ ‫ﻓﻲ‬ ‫اﻟدم‬ ‫اﻧﺳﯾﺎب‬ ‫اﻻﺳﺗﻣرارﯾﺔ‬ ‫ﻟﻣﻌﺎدﻟﺔ‬ ‫اﻟﺗطﺑﯾﻘﺎت‬ ‫أﺣد‬
‫و‬ ‫اﻟدﻗﯾﻘﺔ‬ ‫اﻻوردة‬ ‫ﻋﺑر‬ ‫رﺟوﻋﮫ‬ ‫و‬ ‫اﻟدﻣوﯾﺔ‬ ‫اﻟﺷﻌﯾرات‬ ‫اﻟﻰ‬ ‫ﺛم‬ ‫اﻟدﻗﯾﻘﺔ‬ ‫و‬ ‫اﻟﻔرﻋﯾﺔ‬
‫اﻟرﺋﯾﺳﯾﺔ‬ ‫و‬ ‫اﻟﻔرﻋﯾﺔ‬.
-‫اﻟ‬ ‫ﻣﻘطﻊ‬ ‫ﻣﺳﺎﺣﺔ‬‫اﻟرﺋﯾﺳﯾﺔ‬ ‫ورﯾد‬8cm2
‫اﻻورطﻲ‬ ‫ﻣﻘطﻊ‬ ‫ﻣﺳﺎﺣﺔ‬ ‫ﻣن‬ ‫أﻛﺑر‬)2.5 cm2
.(
-‫اﻟﺷراﯾﯾن‬ ‫ﻓﻲ‬ ‫اﻟﻣوﺟودة‬ ‫اﻟدم‬ ‫ﻛﻣﯾﺔ‬ ‫ﻣن‬ ‫أﻛﺑر‬ ‫اﻻوردة‬ ‫ﻓﻲ‬ ‫اﻟﻣوﺟودة‬ ‫اﻟدم‬ ‫ﻛﻣﯾﺔ‬.
-‫اﻟرﺋﯾﺳﻲ‬ ‫اﻟورﯾد‬ ‫ﻓﻲ‬ ‫اﻟدم‬ ‫ﺳرﻋﺔ‬ ‫ﻣن‬ ‫أﻛﺑر‬ ‫اﻻورطﻲ‬ ‫ﻓﻲ‬ ‫اﻟدم‬ ‫ﺳرﻋﺔ‬.
-‫اﻻورطﻲ‬ ‫ﻋﻧد‬ ‫ﯾﻣﻛن‬ ‫ﻣﺎ‬ ‫أﻛﺑر‬ ‫ﺗﻛون‬ ‫اﻟدم‬ ‫ﺳرﻋﺔ‬30cm/s
-‫ﺗﻛون‬ ‫ﺣﺗﻰ‬ ً‫ﺎ‬‫ﺗدرﯾﺟﯾ‬ ‫اﻟدم‬ ‫ﺳرﻋﺔ‬ ‫ﺗﻘل‬0.3mm/s‫ﺗﻔﺳﯾر‬ ‫و‬ ‫اﻟدﻣوﯾﺔ‬ ‫اﻟﺷﻌﯾرات‬ ‫ﻓﻲ‬
‫و‬ ‫ﻛﺑﯾرة‬ ‫ﻟﮭﺎ‬ ‫اﻟﻛﻠﯾﺔ‬ ‫اﻟﻣﻘطﻊ‬ ‫ﻣﺳﺎﺣﺔ‬ ‫ﻓﺎن‬ ‫ﺑﺎﻟﺗﺎﻟﻲ‬ ‫و‬ ً‫ا‬‫ﺟد‬ ‫ﻛﺑﯾر‬ ‫اﻟﺷﻌﯾرات‬ ‫ﻋدد‬ ‫أن‬ ‫ھو‬ ‫ذﻟك‬
‫اﻟﻛﺑﯾرة‬ ‫اﻟﻣﺳﺎﺣﺔ‬ ‫ﻋﻧد‬ ‫ﺻﻐﯾرة‬ ‫ﺗﻛون‬ ‫اﻟدم‬ ‫ﺳرﻋﺔ‬ ‫ﻓﺈن‬ ‫اﻻﺳﺗﻣرارﯾﺔ‬ ‫ﻟﻣﻌﺎدﻟﺔ‬ ً‫ﺎ‬‫ﺗﺑﻌ‬.
‫ﺑﺮ‬ ‫ﻣﻌــﺎدﻟﺔ‬‫ﻧ‬‫ﻮﻟﻠ‬‫ﻲ‬Bernoulli Equation
‫اﻵﺗﻲ‬ ‫ﻋﻠﻰ‬ ‫ﺗﻧص‬ ‫ﺑرﻧوﻟﻠﻲ‬ ‫ﻧظرﯾﺔ‬ ‫إن‬:‫و‬ ‫اﻟﺣرﻛﺔ‬ ‫طﺎﻗﺔ‬ ‫و‬ ‫اﻟﺿﻐط‬ ‫طﺎﻗﺔ‬ ‫ﻣﺟﻣوع‬ ‫إن‬
‫اﻟوﺿﻊ‬ ‫طﺎﻗﺔ‬)‫اﻟﻛﻠﯾﺔ‬ ‫اﻟطﺎﻗﺔ‬(‫ﯾظل‬ ‫ﻣﻌﯾن‬ ‫اﻟﻣﺳﺎر‬ ‫ﻓﻲ‬ ‫ﯾﺳري‬ ‫ﻣﺎ‬ ‫ﻣﺎﺋﻊ‬ ‫ﻣن‬ ‫ﺟﺳﯾم‬ ‫ﻷي‬
‫ﻣن‬ ‫طﺎﻗﺔ‬ ‫اﻛﺗﺳﺎب‬ ‫أو‬ ‫ﻓﻘد‬ ‫ھﻧﺎك‬ ‫ﯾﻛن‬ ‫ﻟم‬ ‫إذا‬ ،‫اﻟﻣﺳﺎر‬ ‫ذﻟك‬ ‫طول‬ ‫ﻋﻠﻰ‬ ‫ﻣﻘطﻊ‬ ‫أي‬ ‫ﻋﻧد‬ ‫ﺛﺎﺑﺗﺎ‬
‫ﻓﺈن‬ ‫آﺧر‬ ‫ﺑﻣﻌﻧﻰ‬ ‫أو‬ ‫اﻟﻣﺳﺎر‬ ‫ذﻟك‬ ‫ﺣول‬ ‫اﻟﺑﯾﺋﺔ‬:
‫اﻟﺿﻐط‬ ‫طﺎﻗﺔ‬+‫اﻟﺣرﻛﺔ‬ ‫طﺎﻗﺔ‬+‫ﻣﻘطﻊ‬ ‫أي‬ ‫ﻋﻧد‬ ً‫ﺎ‬‫ﺛﺎﺑﺗ‬ ‫ﺗﺳﺎوي‬ ‫اﻟوﺿﻊ‬ ‫طﺎﻗﺔ‬
The force of the lower part of the fluid is P1A1. The work done by this
force is given by, WF1 x1 P1 A1 x1 P1V
where V is the volume of the lower part of the fluid. Similarly the force of the upper
part of the fluid is P2A2. The work done by this force is negative since the fluid force
is opposite to the displacement and is given by,
W2 F2 x2 P2 A2 x2 P2 V
The volume V in the lower and upper part of the fluid is the same. Therefore the net
work done in time t is, W (P1 P2 )V
The change in kinetic energy is given by K 1/2 m v1
2
m v2
2

4. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
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The change in potential energy is given by U mgy2 mgy1
From the total energy theorem, W K U
Divide both sides by V , and substitute for m/ V 
‫ﻣﺛﺎل‬:-‫ﺧزان‬‫ﻛﺑﯾر‬‫ﻣﻣﻠوء‬‫ﺑﺎﻟﻣﺎء‬‫ﯾظﮭر‬‫ﺛﻘب‬‫ﺻﻐﯾر‬‫ﻓﻲ‬‫ﺟﺎﻧﺑﮭﺎ‬‫ﻋﻧد‬‫ﻧﻘطﺔ‬16m
‫ﺗﺣت‬‫ﻣﺳﺗوى‬‫اﻟﻣﯾﺎه‬.‫إذا‬‫ﻛﺎن‬‫ﻣﻌدل‬‫اﻟﺗدﻓﻖ‬‫ﻣن‬‫ﺗﺳرب‬‫ھو‬2.5 x 10-3
m3/min،‫أوﺟد‬
)‫أ‬(‫اﻟﺳرﻋﺔ‬‫اﻟﺗﻲ‬‫ﺗﻐﺎدر‬‫اﻟﻣﯾﺎه‬‫ﻓﻲ‬‫ﺣﻔرة‬.)‫ب‬(‫وﻗطر‬‫اﻟﺛﻘب‬.
‫اﻟﺣــــل‬:
‫اﻟﻠزوﺟﺔ‬Viscosity:-
‫ﻛﻌﺎﺋﻖ‬ ‫ﺗﻌﻣل‬ ‫ھﻲ‬ ‫و‬ ‫طﺑﻘﺎﺗﮫ‬ ‫اﺣﺗﻛﺎك‬ ‫ﻋن‬ ‫ﻧﺎﺷﺋﮫ‬ ‫ھﻲ‬ ‫و‬ ‫اﻟﻣﺎﺋﻊ‬ ‫ﺧواص‬ ‫ﻣن‬ ‫ﺧﺎﺻﯾﺔ‬ ‫ھﻲ‬
‫اﻧﺳﯾﺎﺑﮫ‬ ‫اﺛﻧﺎء‬ ‫اﻟﻣﺎﺋﻊ‬ ‫ﻟﺣرﻛﺔ‬.
‫ﻣن‬ ‫ﯾﺗﻛون‬ ‫ﻣﺎﺋﻊ‬ ‫ﻟدﯾﻧﺎ‬ ‫أن‬ ‫ﻧﻔرض‬‫ﻣﻧﮭﺎ‬ ‫ﻛل‬ ‫ﻣﺳﺎﺣﺔ‬ ‫طﺑﻘﺎت‬)A(‫ﺑﺎﻟﺷﻛل‬ ‫ﻣوﺿﺢ‬ ‫ھو‬ ‫ﻛﻣﺎ‬

5. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
GENERAL PHYSICS 2016 ‫اﻟﻤﻮاﺋﻊ‬ ‫ﻣﯿﻜﺎﻧﯿﻜﺎ‬:
61
‫اﻓﻘﯾﺔ‬ ‫ﻗوة‬ ‫اﺛرت‬ ‫ﻓﺈن‬)F(ً‫ﺎ‬‫ﺗدرﯾﺟﯾ‬ ‫ﺗﺗﺣرك‬ ‫ﺳوف‬ ‫اﻟﺳﺎﺋل‬ ‫طﺑﻘﺎت‬ ‫ﻓﺈن‬ ‫اﻟﻌﻠﯾﺎ‬ ‫اﻟطﺑﻘﺔ‬ ‫ﻋﻠﻰ‬
‫ﺣﯾث‬ ‫اﻟﺳﻔﻠﻰ‬ ‫اﻟطﺑﻘﺔ‬ ‫إﻟﻰ‬ ‫ﻧﺻل‬ ‫ﺣﺗﻰ‬ ‫ﺗﺳﺑﻘﮭﺎ‬ ‫اﻟﺗﻰ‬ ‫ﻣن‬ ‫أﻗل‬ ‫ﺑﺳرﻋﺔ‬ ‫ﺗﺗﺣرك‬ ‫ﻣﻧﮭﺎ‬ ‫ﻛل‬
ً‫ا‬‫ﺻﻔر‬ ‫ﺗﺳﺎوي‬ ‫ﺳرﻋﺗﮭﺎ‬ ‫ﺗﻛون‬.
‫ﯾﻛون‬ ‫ﺑﺎﻟﺗﺎﻟﻲ‬ ‫و‬ⱱ = Fy/ɳA → ɳ = (F/A)/(ⱱ/y)
‫ﺣﯾث‬:-
ɳ‫ھﻲ‬ ‫وﺣدﺗﮫ‬ ‫و‬ ‫اﻟﻠزوﺟﺔ‬ ‫ﻣﻌﺎﻣل‬(N.s/m2
)‫ھﻲ‬ ‫اﻟﺷﺎﺋﻌﺔ‬ ‫اﻟﻠزوﺟﺔ‬ ‫وﺣدات‬ ‫ﻟﻛن‬ ‫و‬
‫ﺳم‬ ‫اﻟﻧظﺎم‬ ‫وﺣدات‬.‫ﺟم‬.‫ث‬)cgs(‫ھﻲ‬ ‫و‬)dyn.s/cm2
(‫ﺑواز‬ ‫ﺗﺳﻣﻰ‬ ‫و‬poise
‫أن‬ ‫أي‬1poise = 1dyn.s.cm-2
= 10-1
N.sm-2
= 10-1
pa.s
‫ﻣﻼﺣظﺎت‬
-‫اﻟﺣرارة‬ ‫درﺟﺔ‬ ‫ﻋﻠﻰ‬ ‫اﻟﻣواﺋﻊ‬ ‫ﻟزوﺟﺔ‬ ‫ﺗﻌﺗﻣد‬
-‫اﻟﺣرارة‬ ‫درﺟﺔ‬ ‫ﺑﺈرﺗﻔﺎع‬ ‫اﻟﺳواﺋل‬ ‫ﻟزوﺟﺔ‬ ‫ﺗﻘل‬
-‫اﻟﺣرارة‬ ‫درﺟﺔ‬ ‫ﺑﺈرﺗﻔﺎع‬ ‫اﻟﻐﺎزات‬ ‫ﻟزوﺟﺔ‬ ‫ﺗزداد‬
‫اﻟﻠزوﺟﺔ‬ ‫ﻣﻌﺎﻣل‬ ‫أن‬ ‫ﻧﻌﺎم‬ ‫أن‬ ‫اﻟﻔﯾد‬ ‫ﻣن‬ ‫ﻟﻌﻠﮫ‬ ‫و‬ɳ‫ﺣرارة‬ ‫درﺟﺔ‬ ‫ﻋﻧد‬ ‫ﻟﻠدم‬37 o
C‫ھو‬)4x10-3
N.s/m2
(‫ھو‬ ‫اﻟﺣرارة‬ ‫درﺟﺔ‬ ‫ﻧﻔس‬ ‫ﻓﻲ‬ ‫اﻟدم‬ ‫ﻟﺑﻼزﻣﺎ‬ ‫و‬ ،)1.5x10-3
N.s/m2
(.
-‫ﯾﺧﺿ‬ ‫ﻻ‬ ‫ﻛﻣﺎﺋﻊ‬ ‫اﻟدم‬ ‫أن‬ ‫ﻧﻼﺣظ‬‫ﺑﯾن‬ ‫اﻟﻌﻼﻗﺔ‬ ‫ﻓﺗﻛون‬ ‫ﺗﺟﺎﻧﺳﮫ‬ ‫ﻟﻌدم‬ ‫وذﻟك‬ ‫ذﻛره‬ ‫ﺳﺑﻖ‬ ‫ﻟﻣﺎ‬ ‫ﻊ‬
‫ﻓﺈن‬ ‫اﻟﻘوة‬ ‫أﺛرﻧﺎﺑﺿﻌف‬ ‫ﻓﺈذا‬ ،‫ﺧطﯾﺔ‬ ‫ﻋﻼﻗﺔ‬ ‫ﻟﯾﺳت‬ ‫اﻟﺳرﻋﺔ‬ ‫و‬ ‫اﻟﻣؤﺛرةﻋﻠﯾﮫ‬ ‫اﻻﻓﻘﯾﺔ‬ ‫اﻟﻘوة‬
‫ﻓــ‬ ‫اﻟﻣﺗوﻗﻌﺔ‬ ‫اﻟﺳرﻋﺔ‬ ‫ﺿﻌف‬ ‫ﻣن‬ ‫أﻛﺑر‬ ‫ﺗﻛون‬ ‫اﻟﻧﺎﺗﺟﺔ‬ ‫اﻟﺳرﻋﺔ‬‫اﻟﻠزوﺟﺔ‬ ‫ﻣﻌﺎﻣل‬ɳ‫ﻋﻧد‬ ‫ﻟﻠدم‬
‫ﺣرارة‬ ‫درﺟﺔ‬37 o
C‫ھو‬)4x10-3
N.s/m2
(‫اﻟدم‬ ‫ﻟﺑﻼزﻣﺎ‬ ‫و‬ ،‫اﻟﺣرارة‬ ‫درﺟﺔ‬ ‫ﻧﻔس‬ ‫ﻓﻲ‬
‫ھو‬)1.5x10-3
N.s/m2
(.
‫ﺑــوازي‬ ‫ﻗﺎﻧون‬Poiseuille's law:-
‫ﻣﺣور‬ ‫ﻋﻧد‬ ‫ﯾﻣﻛن‬ ‫ﻣﺎ‬ ‫اﻛﺑر‬ ‫ﺗﻛون‬ ‫اﻻﻧﺳﯾﺎب‬ ‫ﺳرﻋﺔ‬ ‫أن‬ ‫ﻧﺟد‬ ‫اﻧﺑوﺑﺔ‬ ‫ﺧﻼل‬ ‫ﻟزج‬ ‫ﻣﺎﺋﻊ‬ ‫اﻧﺳﯾﺎب‬ ‫ﻋﻧد‬
‫اﻟﺳرﻋﺔ‬ ‫ﺗﻧﻌدم‬ ‫ﺣﯾث‬ ‫اﻻﻧﺑوﺑﺔ‬ ‫ﺟدار‬ ‫ﻣن‬ ‫اﻗﺗرﺑﻧﺎ‬ ‫و‬ ‫اﻟﻣﺣور‬ ‫اﺑﺗﻌدﻧﺎﻋن‬ ‫ﻛﻠﻣﺎ‬ ‫ﺗﻘل‬ ‫و‬ ‫اﻻﻧﺑوﺑﺔ‬.
‫ﻟز‬ ‫ﻣﺎﺋﻊ‬ ‫اﻧﺳﯾﺎب‬ ‫ﺳرﻋﺔ‬‫ج‬‫طوﻟﮭﺎ‬ ‫اﻻﻧﺑوﺑﺔ‬ ‫ﻣﺣور‬ ‫ﻋﻧد‬(L)‫ﻗطرھﺎ‬ ‫ﻧﺻف‬ ‫و‬)r(‫اﻟﺿﻐط‬ ‫ﻓرق‬ ‫و‬
‫طرﻓﯾﮭﺎ‬ ‫ﺑﯾن‬)∆p = p1 - p2(‫ھﻲ‬:-

6. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
GENERAL PHYSICS 2016 ‫اﻟﻤﻮاﺋﻊ‬ ‫ﻣﯿﻜﺎﻧﯿﻜﺎ‬:
62
‫ﻟﻼﻧﺳﯾﺎب‬ ‫ﺳرﻋﺔ‬ ‫اﻗﺻﻰ‬ⱱm = ∆p r2
/4ɳL
‫اﻻﻧﺳﯾﺎب‬ ‫ﺳرﻋﺔ‬ ‫ﻣﺗوﺳط‬)ⱱ(‫ﺣﯾث‬
ⱱ = (ⱱm + 0)/2 = ⱱm/2 = 1/2(∆p r2
/4ɳL) → ⱱ =∆p r2
/8ɳL
‫اﻻﻧﺳﯾﺎب‬ ‫ﻣﻌدل‬)Q(‫ھـو‬:-Q = Aⱱ = A ⱱm/2
Q = r2
(∆p r2
/8ɳL) → Q = ∆p r4
/8ɳL → Q = ∆p /(8ɳL/ r4
)
R = 8ɳL/ r4
‫ﺣﯾث‬R‫ﻓﯾﮫ‬ ‫اﻟﻣﺎﺋﻊ‬ ‫اﻧﺳﯾﺎب‬ ‫اﻋﺎﻗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺗﻌﻣل‬ ‫و‬ ‫اﻻﻧﺑوﺑﺔ‬ ‫ﻣﻘﺎوﻣﺔ‬
‫وﺣدﺗﮭﺎ‬ ‫و‬pa.s/m3
= N.s/m5
Q = ∆p/R
*‫اﻻﻧﺳﺎن‬ ‫ﺟﺳم‬ ‫ﻓﻲ‬ ‫اﻟدم‬ ‫اﻧﺳﯾﺎب‬
‫ﺑوازوي‬ ‫ﻗﺎﻧون‬ ‫وﻓﻖ‬ ‫اﻟدﻣوﯾﺔ‬ ‫اﻻوﻋﯾﺔ‬ ‫ﻓﻲ‬ ‫اﻟدم‬ ‫ﯾﻧﺳﺎب‬
*‫طوﻟﮫ‬ ‫دﻣوي‬ ‫وﻋﺎء‬ ‫ﻓﻲ‬ ‫اﻟدم‬ ‫اﻧﺳﯾﺎب‬ ‫ﻣﻌدل‬L‫ﻗطره‬ ‫ﻧﺻف‬ ‫و‬r‫طرﻓﯾﮫ‬ ‫ﺑﯾن‬ ‫اﻟﺿﻐط‬ ‫ﻓرق‬ ‫و‬
∆p = p1-p2‫ھو‬Q = ∆p r4
/8ɳL‫و‬Q = ∆p/R‫و‬R = 8ɳL/ r4
‫اﻟﺿﻐط‬ ‫ﻓرق‬ ‫ﺛﺑوت‬ ‫ﻋﻧد‬Q ∝ r4
Q2/Q1 = r2
4
/r1
4
= (r2/r1)4
‫اﻟﺷرﯾﺎن‬ ‫ﻗطر‬ ‫ﺛﺑوت‬ ‫ﻋﻧد‬Q ∝ ∆p
Q2/Q1 = ∆p2/∆p1
‫اﻻﻧﺳﯾﺎب‬ ‫ﻣﻌدل‬ ‫ﺛﺑوت‬ ‫ﻋﻧد‬∆p ∝ 1/r4
‫اﻟﺿﻐط‬ ‫ﻓﻲ‬ ‫اﻟﻔرق‬ ‫زاد‬ ‫اﻟﻘطر‬ ‫ﻧﺻف‬ ‫ﻗل‬ ‫ﻛﻠﻣﺎ‬∆p2/∆p1 = r1
4
/r2
4
= (r1/r2)4
‫ﻣﻼﺣظﺎت‬:-
‫اﻟﺷﻌﯾرات‬ ‫ھذه‬ ‫ﻻن‬ ‫ﻟك‬ ‫و‬ ‫اﻟدﻣوﯾﺔ‬ ‫اﻟﺷﻌﯾرات‬ ‫ﺧﻼل‬ ‫ﻣروره‬ ‫ﻋﻧد‬ ً‫ا‬‫ﻛﺛﯾر‬ ‫اﻟدم‬ ‫ﺿﻐط‬ ‫ﯾﻧﺧﻔض‬ ‫ﻻ‬
‫اﻟﺗوازي‬ ‫ﻋﻠﻰ‬ ‫ﻣوﺻﻠﺔ‬ ‫و‬ ‫اﻛﺑر‬ ‫ﻋددھﺎ‬.
*‫اﻻﻧﺳﯾﺎب‬ ‫ﻣﻌدل‬ ‫ﻛﺎن‬ ‫إذا‬)Q(‫اﻟواﺣدة‬ ‫اﻟدﻣوﯾﺔ‬ ‫اﻟﺷﻌﯾرة‬ ‫ﻓﻲ‬ ‫اﻻﻧﺳﯾﺎب‬ ‫ﻣﻌدل‬ ‫و‬q‫ﻓﺈن‬:-
‫ﺣﯾث‬n‫اﻟدﻣوﯾﺔ‬ ‫اﻟﺷﻌﯾرات‬ ‫ﻋدد‬Q = nq → n = Q/q →

7. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
GENERAL PHYSICS 2016 ‫اﻟﻤﻮاﺋﻊ‬ ‫ﻣﯿﻜﺎﻧﯿﻜﺎ‬:
63
‫أﻣﺛﻠﮫ‬:

8. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
GENERAL PHYSICS 2016 ‫اﻟﻤﻮاﺋﻊ‬ ‫ﻣﯿﻜﺎﻧﯿﻜﺎ‬:
64
‫ﻣﺛﺎل‬4
:-
‫اﻟﺣل‬:-

9. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
GENERAL PHYSICS 2016 ‫اﻟﻤﻮاﺋﻊ‬ ‫ﻣﯿﻜﺎﻧﯿﻜﺎ‬:
65
→→

10. ‫ﺍﻹﺳﻼﻣﻴﺔ‬‫ﺍﻷﲰﺮﻳﺔ‬‫ﺍﳉﺎﻣﻌﺔ‬‫ا‬
GENERAL PHYSICS 2016 ‫اﻟﻤﻮاﺋﻊ‬ ‫ﻣﯿﻜﺎﻧﯿﻜﺎ‬:
66