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
Ok i got a question I'm not asking how gravity works. I would like to know why gravity works. like why is gravity the way it is. What is the true nature of gravity?
An automobile traveling with an initial velocity of 25m/s is accelerated to 35m/s in 6s,the wheel of the automobile is 80cm in diameter. find
* The angular acceleration
a postmodernist would say that he did not discover them, he made them up and they're not actually a reality in itself, but a mere construct by which we decided to observe the word around us
elo
how?
Qhoshe
Besides his work on universal gravitation (gravity), Newton developed the 3 laws of motion which form the basic principles of modern physics. His discovery of calculus led the way to more powerful methods of solving mathematical problems. His work in optics included the study of white light and
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