An air conditioning system is being designed to supply air at a gauge pressure of 0.054 Pa at a temperature of
$20\phantom{\rule{0.2em}{0ex}}\text{\xb0}\text{C}.$ The air is sent through an insulated, round conduit with a diameter of 18.00 cm. The conduit is 20-meters long and is open to a room at atmospheric pressure 101.30 kPa. The room has a length of 12 meters, a width of 6 meters, and a height of 3 meters. (a) What is the volume flow rate through the pipe, assuming laminar flow? (b) Estimate the length of time to completely replace the air in the room. (c) The builders decide to save money by using a conduit with a diameter of 9.00 cm. What is the new flow rate?
Strategy
Assuming laminar flow, Poiseuille’s law states that
We need to compare the artery radius before and after the flow rate reduction. Note that we are given the diameter of the conduit, so we must divide by two to get the radius.
Solution
Assuming a constant pressure difference and using the viscosity
$\eta =0.0181\phantom{\rule{0.2em}{0ex}}\text{mPa}\cdot \text{s}$ ,
Thus, the radius of the conduit decreases by half reduces the flow rate to 6.25% of the original value.
Significance
In general, assuming laminar flow, decreasing the radius has a more dramatic effect than changing the length. If the length is increased and all other variables remain constant, the flow rate is decreased:
Water pressure in homes is sometimes lower than normal during times of heavy use, such as hot summer days. The drop in pressure occurs in the water main before it reaches individual homes. Let us consider flow through the water main as illustrated in
[link] . We can understand why the pressure
${p}_{1}$ to the home drops during times of heavy use by rearranging the equation for flow rate:
In this case,
${p}_{2}$ is the pressure at the water works and
R is the resistance of the water main. During times of heavy use, the flow rate
Q is large. This means that
${p}_{2}-{p}_{1}$ must also be large. Thus
${p}_{1}$ must decrease. It is correct to think of flow and resistance as causing the pressure to drop from
${p}_{2}$ to
${p}_{1}$ . The equation
${p}_{2}-{p}_{1}=RQ$ is valid for both laminar and turbulent flows.
Questions & Answers
A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be
vector has both magnitude & direction but scalar has only magnitude
Manash
my marunong ba dto mag prove ng geometry
ron
how do I find resultant of four forces at a point
Inusah
use the socatoa rule
kingsley
draw force diagram, then work out the direction of force.
Rongfang
In a closed system of forces... Summation of forces in any direction or plane is zero... Resolve if there is a need to then add forces in a particular plane or direction.. Say the x direction... Equate it tk zero
a system of mechanics based of Newton laws motion this is easy difenation of mean...
Arzoodan
what is the meaning of single term,mechanics?
jyotirmayee
mechanics is the science related to the behavior of physical bodies when some external force is applied to them
Lalita
SO ASK
What is Newtonian mechanics in physics?
Newtonian physics, also calledNewtonian or classical mechanics, is the description of mechanical events—those that involve forces acting on matter—using the laws of motion and gravitation formulated in the late seventeenth century by English physicist
Suleiman
can any one send me the best reference book for physics?
Prema
concept of physics by HC verma, Fundamentals of Physics, university of physics
Bhaskar
tq u.
Prema
these are the best physics books one can fond both theory and applications.
Bhaskar
can any one suggest best book for maths with lot of Tricks?
Vivek
what is the water height in barometer?
SUNEELL
13.5*76 cm. because Mercury is 13.5 times dense than Mercury
LOVE
water is 13.5 times dense than the Mercury
LOVE
plz tell me frnds the best reference book for physics along with the names of authors.
Prema
i recomended the reference book for physics from library University of Dublin or library Trinity college
Arzoodan
A little help here...
.
1. Newton's laws of Motion, are they applicable to motions of all speeds?
2.state the speeds which are applicable to Newtons laws of Motion
Derek
mechanics which follows Newtons law
Manash
The definition of axial and polar vector .
Arpita
polar vector which have a starting point or pt. of applications is,force,displacement
jyotirmayee
axial vector represent rotational effect and act along the axis of rotation b
It states that, " If two vectors are represented in magnitude and direction by the two sides of a triangle, then their resultant is represented in magnitude and direction by the third side of the triangl " .