Is pipe friction more important than velocity in determining pumping pressure?

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The discussion centers on the relationship between pipe friction, velocity, and pumping pressure. It highlights that while pumping power is proportional to volume rate, the friction in smaller pipes increases pressure requirements. A larger pipe may have lower velocity, but the pressure must still account for increased friction in narrower pipes. The assumption of constant volumetric flow rate leads to the conclusion that pressure differences are significant due to varying pipe diameters. Ultimately, pipe friction plays a crucial role in determining pumping pressure, often outweighing the effects of velocity.
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Homework Statement


in the notes , we can see that the formula of pumping power per unit time is (pressure)(volume rate),
so pumping power is directly proportional to volume rate ...
but , the author told that the pumping power is proportional to the length of pipe , and inversely proportional 4th power of radius ...
As we can see , the volume rate has the formula of [delta(P) (R^4) / (8 μ L ) ] , so when R increases by factor of 2 , the volume rate should increases by factor of 16 , thus the pumping power is 16 times the pipe with radius R , am i right ? however , in diagram 8-14, it's different

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No, you are not right. No where does it say anything about changing the pump to a larger size.

Diagram 8-14 : the assumption is that the volumetric flow rate is constant.
 
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256bits said:
No, you are not right. No where does it say anything about changing the pump to a larger size.

Diagram 8-14 : the assumption is that the volumetric flow rate is constant.
assuming the volumetric flow rate in both pipe is constant , thus W / time = P (volume rate ) ... now , only thr pressure is changing ...since in the large pipe , the velocity of water is slow , so the pressure is high ... thus , the pumping power should be higher than the thin pipe , right ?
 
foo9008 said:
assuming the volumetric flow rate in both pipe is constant , thus W / time = P (volume rate ) ... now , only thr pressure is changing ...since in the large pipe , the velocity of water is slow , so the pressure is high ... thus , the pumping power should be higher than the thin pipe , right ?
You are forgetting that the pipe friction is greater in the smaller diameter pipe.
The pump has to produce a greater pressure pumping through a smaller pipe.
 
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256bits said:
You are forgetting that the pipe friction is greater in the smaller diameter pipe.
The pump has to produce a greater pressure pumping through a smaller pipe.
the pipe friction outweigh the (v^2) / 2g ? , so the the pumping pressure in small pipe is higher?
 
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