[Fluid Mechanics] Water Flow in a Hose

[Aprileo]

Homework Statement

Given:
Water flows through a 15.24m long, 1.6cm diameter hose.

pressure at the outdoor tap = 275.8kPa

volumetric flowrate, Q = 7.5e-4 m^3/s (i.e. 7.5L for 10 seconds)

viscosity of water, μ = 0.001 Pa*s
density of water, ρ = 1000 kg/m^3

Look for: the roughness of the hose

Homework Equations

Renolds number:

Darcy equation:

Moody chart:

The Attempt at a Solution

I have calculated Renolds number = 7958 ==> turbulent flow

I used Darcy equation and found out the friction factor, f, is great than 1.
I am confused and stuck here.
I must have used the wrong formula or missed some important steps.

Please help me by providing some advice, double checking my work or giving some steps would be greatly appreciated!

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Chestermiller]

Show us your work.

 

[Aprileo]

volumetric flowrate = Q = 7.5e-4 m^3/s
D = diameter = 0.016m
velocity = V =volumetric flow rate/cross sectional area = Q/(pi*D^2*0.25) = 0.497 m/s

density = ρ = 1000kg/m^3
viscosity = μ = 0.001 Pa*s
Renolds number = Re = (density*velocity*diameter)/viscosity = 7958 > 2100 ==> turbulent flow

L = length of the hose = 15.24m
pressure at outdoor tap = ΔP = 275.8kPa
friction factor = f = (2*ΔP*D) / (L*ρ*V^2) = 2.34 ==> doesn't make sense and I'm stuck here.

 

[Chestermiller]

Check your velocity calculation. I get 3.73 m/s.

 

[Aprileo]

Thank you very much, Chestermiller!

you are correct, V = 3.73 m/s,
problem solved.