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If we want to pump air or water through a pipe, common sense tells us that it will be easier to move a larger quantity more quickly through a fatter pipe. Quantitatively, we can define the
resistance, 
, which is the ratio of the pressure difference
produced by the pump to the rate of flow. A fatter pipe will have a lower resistance. Two pipes can be used in parallel, for instance when you turn on the water both in the kitchen and in the
bathroom, and in this situation, the two pipes let more water flow than either would have let flow by itself, which tells us that they act like a single pipe with some lower resistance. The
equation for their combined resistance is 
.
Analyze the case where one resistance is finite, and the other infinite, and give a physical interpretation. Likewise, discuss the case where one is finite, but the other is
infinitesimal.
, which is the ratio of the pressure difference
produced by the pump to the rate of flow. A fatter pipe will have a lower resistance. Two pipes can be used in parallel, for instance when you turn on the water both in the kitchen and in the
bathroom, and in this situation, the two pipes let more water flow than either would have let flow by itself, which tells us that they act like a single pipe with some lower resistance. The
equation for their combined resistance is .
Analyze the case where one resistance is finite, and the other infinite, and give a physical interpretation. Likewise, discuss the case where one is finite, but the other is
infinitesimal.
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