<< Chapter < Page Chapter >> Page >
Q = P 2 P 1 R size 12{Q= { {P rSub { size 8{2} } - P rSub { size 8{1} } } over {R} } } {}


P 2 P 1 = R Q , size 12{P rSub { size 8{2} } - P rSub { size 8{1} } =R`Q} {}

where, in this case, P 2 size 12{P rSub { size 8{2} } } {} is the pressure at the water works and R size 12{R} {} is the resistance of the water main. During times of heavy use, the flow rate Q size 12{Q} {} is large. This means that P 2 P 1 size 12{P rSub { size 8{2} } - P rSub { size 8{1} } } {} must also be large. Thus P 1 size 12{P rSub { size 8{1} } } {} must decrease. It is correct to think of flow and resistance as causing the pressure to drop from P 2 size 12{P rSub { size 8{2} } } {} to P 1 size 12{P rSub { size 8{1} } } {} . P 2 P 1 = R Q size 12{P rSub { size 8{2} } - P rSub { size 8{1} } =R`Q} {} is valid for both laminar and turbulent flows.

Figure shows the water distribution system from a water works to homes around that area. The pressure at the pipeline near the water works is shown to have a pressure P two and the pressure at the dividing point were the pipe line splits to corresponding houses the pressure is shown as P one.
During times of heavy use, there is a significant pressure drop in a water main, and P 1 supplied to users is significantly less than P 2 created at the water works. If the flow is very small, then the pressure drop is negligible, and P 2 P 1 size 12{P rSub { size 8{2} } approx P rSub { size 8{1} } } {} .

We can use P 2 P 1 = R Q size 12{P rSub { size 8{2} } - P rSub { size 8{1} } =R`Q} {} to analyze pressure drops occurring in more complex systems in which the tube radius is not the same everywhere. Resistance will be much greater in narrow places, such as an obstructed coronary artery. For a given flow rate Q size 12{Q} {} , the pressure drop will be greatest where the tube is most narrow. This is how water faucets control flow. Additionally, R size 12{Q} {} is greatly increased by turbulence, and a constriction that creates turbulence greatly reduces the pressure downstream. Plaque in an artery reduces pressure and hence flow, both by its resistance and by the turbulence it creates.

[link] is a schematic of the human circulatory system, showing average blood pressures in its major parts for an adult at rest. Pressure created by the heart’s two pumps, the right and left ventricles, is reduced by the resistance of the blood vessels as the blood flows through them. The left ventricle increases arterial blood pressure that drives the flow of blood through all parts of the body except the lungs. The right ventricle receives the lower pressure blood from two major veins and pumps it through the lungs for gas exchange with atmospheric gases – the disposal of carbon dioxide from the blood and the replenishment of oxygen. Only one major organ is shown schematically, with typical branching of arteries to ever smaller vessels, the smallest of which are the capillaries, and rejoining of small veins into larger ones. Similar branching takes place in a variety of organs in the body, and the circulatory system has considerable flexibility in flow regulation to these organs by the dilation and constriction of the arteries leading to them and the capillaries within them. The sensitivity of flow to tube radius makes this flexibility possible over a large range of flow rates.

Figure is a schematic diagram of the circulatory system. The lungs, heart, arteries and vein systems are shown. The blood is shown to flow from the left atrium through the arteries, then through the veins and back to the right atrium. The flow is also shown from right atrium to the lungs and from lungs back to left atrium. All parts of the system are labeled. Pressure various points of the system all along the movement of blood across various parts are also marked.
Schematic of the circulatory system. Pressure difference is created by the two pumps in the heart and is reduced by resistance in the vessels. Branching of vessels into capillaries allows blood to reach individual cells and exchange substances, such as oxygen and waste products, with them. The system has an impressive ability to regulate flow to individual organs, accomplished largely by varying vessel diameters.

Each branching of larger vessels into smaller vessels increases the total cross-sectional area of the tubes through which the blood flows. For example, an artery with a cross section of 1 cm 2 size 12{1`"cm" rSup { size 8{2} } } {} may branch into 20 smaller arteries, each with cross sections of 0.5 cm 2 size 12{0 "." 5`"cm" rSup { size 8{2} } } {} , with a total of 10 cm 2 size 12{"10"`"cm" rSup { size 8{2} } } {} . In that manner, the resistance of the branchings is reduced so that pressure is not entirely lost. Moreover, because Q = A v ¯ size 12{Q=A { bar {v}}} {} and A increases through branching, the average velocity of the blood in the smaller vessels is reduced. The blood velocity in the aorta ( diameter = 1 cm size 12{"diameter"=1`"cm"} {} ) is about 25 cm/s, while in the capillaries ( 20 μ m in diameter) the velocity is about 1 mm/s. This reduced velocity allows the blood to exchange substances with the cells in the capillaries and alveoli in particular.

Questions & Answers

what is heat
Ojo Reply
heat is the transfer of internal energy from one point to another
what is a wave
Williams Reply
wave means. A field of study
what are Atoms
is the movement back and front or up and down
how ?
wave is a disturbance that transfers energy through matter or space with little or no associated mass.
A wave is a motion of particles in disturbed medium that carry energy from one midium to another
an atom is the smallest unit( particle) of an element that bares it's chemical properties
what is electromagnetic induction?
How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
Larissa Reply
How do you convert 0.0045kgcm³ to the si unit?
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
Falana Reply
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Alright Thank you
Which one is the Bose-Einstein
can you explain what plasma and the I her one you mentioned
u can say sun or stars are just the state of plasma
but the are more than seven
list it out I wanna know
what the meaning of continuum
Akhigbe Reply
What state of matter is fire
Thapelo Reply
fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Isn`t fire the plasma state of matter?
all this while I taught it was plasma
How can you define time?
Thapelo Reply
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
unpredictable? but I can say after one o'clock its going to be two o'clock predictably!
how can we define vector
I would define it as having a magnitude (size)with a direction. An example I can think of is a car traveling at 50m/s (magnitude) going North (direction)
as for me guys u would say time is quantity that measures how long it takes for a specific condition to happen e.g how long it takes for the day to end or how it takes for the travelling car to cover a km.
what is the relativity of physics
Paul Reply
How do you convert 0.0045kgcm³ to the si unit?
What is the formula for motion
Anthony Reply
V=u+at V²=u²-2as
they are eqns of linear motion
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
Explain dopplers effect
Jennifer Reply
Not yet learnt
Explain motion with types
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Alabi Reply
Scalar quantity Because acceleration has only magnitude
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
its a scalar quantity
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
respect to prevailing force
What is the difference between impulse and momentum?
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
Or I = m(v-u)
the tendency of a body to maintain it's inertia motion is called momentum( I believe you know what inertia means) so for a body to be in momentum it will be really hard to stop such body or object..... this is where impulse comes in.. the force applied to stop the momentum of such body is impulse..
Calculation of kinetic and potential energy
dion Reply
K.e=mv² P.e=mgh
K is actually 1/2 mv^2
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
what is sound wave
Nworu Reply
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
its a longitudnal wave which is associted wth compresion nad rearfractions
what is power
it's also a capability to do something or act in a particular way.
Newton laws of motion
power also known as the rate of ability to do work
power means capabilty to do work p=w/t its unit is watt or j/s it also represents how much work is done fr evry second
Practice Key Terms 5

Get the best College physics course in your pocket!

Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?