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

[foo9008]

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

Homework Equations

The Attempt at a Solution

 

[256bits]

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.

 

[foo9008]

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 ?

 

[256bits]

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.

 

[foo9008]

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?