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

to

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

Prove that 1/d+1/v=1/f
James Reply
What interference
Moyinoluwa Reply
What is a polarized light called?
Moyinoluwa
what is a half life
Mama Reply
the time taken for a radioactive element to decay by half of its original mass
ken
what is radioactive element
mohammed
Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
Justice
state the laws of refraction
Fabian
state laws of reflection
Fabian
Why does a bicycle rider bends towards the corner when is turning?
Mac
When do we say that the stone thrown vertically up wards accelerate negatively?
Mac
Give two importance of insulator placed between plates of a capacitor.
Mac
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
Mac
when was the name taken from
Biola Reply
retardation of a car
Biola
when was the name retardation taken
Biola
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Sphere
Atomic transmutation
Basirat Reply
An atom is the smallest indivisible particular of an element
mosco Reply
what is an atomic
Awene Reply
reference on periodic table
Titus Reply
what Is resonance?
Mozam Reply
phenomena of increasing amplitude from normal position of a substance due to some external source.
akif
What is a black body
Amey Reply
Black body is the ideal body can absorb and emit all radiation
Ahmed
the emissivity of black body is 1. it is a perfect absorber and emitter of heat.
Busayo
Why is null measurement accurate than standard voltmeter
Neemat Reply
that is photoelectric effect ?
Sabir Reply
It is the emission of electrons when light hits a material
Anita
Yeah
yusuf
is not just a material
Neemat
it is the surface of a metal
Neemat
what is the formula for time of flight ,maxjmum height and range
agangan Reply
what is an atom
Awene
an atom is the smallest particle of a element which can take part in chemical reaction.
Israel
how does a lightning rod protect a building from damage due to lightning ?
Faith Reply
due to its surface lustre but due to some factors it can corrode but not easily as it lightning surface
babels
pls what is mirage
babels
light rays bend to produce a displaced image of distant objects; it's an natural & optical phenomenon......
Deepika
what is the dimensional formula for torque
Otto Reply
L2MT-2
Jolly
same units of energy
Baber
what is same units of energy?
Baber
Nm
Sphere
Ws
Sphere
CV
Sphere
M L2 T -2
Dokku
it is like checking the dimension of force. which is ML2T-2
Busayo
ML2T-2
Joshua
M L2 T-2
Samuel
what is the significance of moment of inertia?
study
Practice Key Terms 5

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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