- #1

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- Homework Statement
- Please see below

- Relevant Equations
- Please see below

For this problem,

My assumption is that the pipe diameter is the same from the council tubby to where the water comes out of the tape.

##P_2 - P_1 ≈ 1 bar ≈ 100000 Pa##

##η ≈ 10^{-3} Pa \cdot s##

##L ≈ 10 m##

##π ≈ 3##

##r ≈ 1 cm ≈ 0.01 m##

However, when I substitute those values into Poiseuille's equation I get ##Q ≈ 0.0375 ≈ 0.04 \frac{m^3}{s}##. When I convert it to ##\frac{L}{min}## I get ##2400 \frac{L}{min}## However, Q should be in the order of ##10 \frac{L}{min}##. My order of magnitude calculation is orders of magnitude off.

I am not sure how to make the calculation more reasonable. If I increase the length to say 100m, it still dose not give a value in between ##10 \frac{L}{min}##.

I am wondering whether my assumption is wrong, that is, the pipe diameter varies from the council tubby to the where the water comes out. I think ##r## should be initially larger than what I said it to be, and there decreases to the value I measured when it reach's the tap cyclinder. However, I am not sure whether it possible to account for that in Poiseuille equation. Maybe I should use Bernoulli equation.

Any guidance would me much appreciated!

Many thanks!

*The mains water pressure at the council tubby (just before it enters a house) is of the order of 1.5 bar. Using Poiseuille equation, estimate the flow rate in a typical home at the kitchen tap. You will need to make reasonable estimates on several parameters, clearly state these assumptions (note that this estimate does not need to agree with your measurement in Q1, but it shouldn’t be orders-of-magnitude different).*My assumption is that the pipe diameter is the same from the council tubby to where the water comes out of the tape.

##P_2 - P_1 ≈ 1 bar ≈ 100000 Pa##

##η ≈ 10^{-3} Pa \cdot s##

##L ≈ 10 m##

##π ≈ 3##

##r ≈ 1 cm ≈ 0.01 m##

However, when I substitute those values into Poiseuille's equation I get ##Q ≈ 0.0375 ≈ 0.04 \frac{m^3}{s}##. When I convert it to ##\frac{L}{min}## I get ##2400 \frac{L}{min}## However, Q should be in the order of ##10 \frac{L}{min}##. My order of magnitude calculation is orders of magnitude off.

I am not sure how to make the calculation more reasonable. If I increase the length to say 100m, it still dose not give a value in between ##10 \frac{L}{min}##.

I am wondering whether my assumption is wrong, that is, the pipe diameter varies from the council tubby to the where the water comes out. I think ##r## should be initially larger than what I said it to be, and there decreases to the value I measured when it reach's the tap cyclinder. However, I am not sure whether it possible to account for that in Poiseuille equation. Maybe I should use Bernoulli equation.

Any guidance would me much appreciated!

Many thanks!

Last edited: