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.
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Why is popo less than atmospheric? Why is popo greater than pipi?
Louise
The old rubber boot shown below has two leaks. To what maximum height can the water squirt from Leak 1? How does the velocity of water emerging from Leak 2 differ from that of Leak 1? Explain your responses in terms of energy.
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The rate of change in angular displacement is defined as angular velocity.
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Lindomar
... that tends to fight for its previous direction when you try to attribute to it an opposite one ou try to stop it.The same thing also happens whe a car goes around a curve, the car it self is designed to a"straight line"(look at the position of its tyres, mainly the back side ones), so...
Lindomar
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