How to Calculate the Length of a Capillary Tube for a Drip-Irrigation Emitter

[maxnormal]

Homework Statement

A drip-irrigation emitter constructed of a coiled capillary tube is inserted into the wall of a drip irrigation line with a constant water pressure of 5 psi. Compute the required length of the emitter’s capillary tube to produce an emitter dripping rate of 2 litres per hour if the capillary tube diameter is 1mm.

Homework Equations

Pressure = Force * Area
Volume of Cylinder = ∏ * Length *Radius^2

The Attempt at a Solution

I converted all the units into SI. I know I need to solve for length of the cylinder, but when I try to equal the cylinder dimensions to 5psi nothing works out. Just don't know how to approach the problem yet. Any help would be appreciated. Thanks.

5 pounds/inch^2 = 34,473.7865 kg/ms^2
2Litres/hour = 5.55x10^-7 m^3/s
diameter = 1mm = 0.001m
radius = 0.001m/2 = 0.0005m

 

[Chestermiller]

Hi Maxnormal. Welcome to Physics Forums!

Are you learning fluid mechanics? Have you learned about the Hagen -Poiseuille viscous flow equation?

Chet

 

[maxnormal]

Hi Maxnormal. Welcome to Physics Forums!

Are you learning fluid mechanics? Have you learned about the Hagen -Poiseuille viscous flow equation?

Chet

Hey! Right now I am learning Soil Physics. And I have not learned of that equation yet. Will I need that equation to solve the problem?

 

[Chestermiller]

Hey! Right now I am learning Soil Physics. And I have not learned of that equation yet. Will I need that equation to solve the problem?

Google it and see if it satisfies your needs.

Chet

 

[HalfLostAndSearching]

Area = ∏ * (0.0005m)^2 = 7.85x10^-7 m^2

Pressure = (5.55x10^-7 m^3/s) / (7.85x10^-7 m^2 * length)
34,473.7865 kg/ms^2 = 5.55x10^-7 m^3/s / (7.85x10^-7 m^2 * length)

Solving for length:
length = (5.55x10^-7 m^3/s) / (34,473.7865 kg/ms^2 * 7.85x10^-7 m^2)
length = 0.0000016 meters

The required length of the emitter's capillary tube is 0.0000016 meters.