To calculate the velocity of water flow in the tubing, we can use the Hagen-Poiseuille equation, which applies to laminar flow. The equation is given by:
Q = (π * r4 * ΔP) / (8 * μ * L)
where:
- Q = volumetric flow rate (m3/s)
- r = radius of the tubing (m)
- ΔP = pressure difference across the length of the tubing (Pa)
- μ = dynamic viscosity of the fluid (Pa·s)
- L = length of the tubing (m)
We know that the viscosity of water at 25°C is approximately 0.00089 Pa·s and the inner diameter of the tubing is 1.14 mm, which gives us a radius (r) of:
r = 1.14 mm / 2 = 0.57 mm = 0.00057 m
Assuming a certain pressure difference and length, we find the velocity v from the volumetric flow rate using the relationship:
v = Q / A
where:
- A = cross-sectional area of the tubing = π * r2
The area (A) can be calculated as:
A = π * (0.00057 m)2 ≈ 1.021 * 10-6 m2
Now, if we assume a pressure difference of, say, 1000 Pa and a length of 1 m, we can substitute these values back into the Hagen-Poiseuille equation to find Q:
Q = (π * (0.00057 m)4 * 1000 Pa) / (8 * 0.00089 Pa·s * 1 m)
Calculating this gives:
Q ≈ 2.158 * 10-9 m3/s
Finally, to find the velocity:
v = Q / A = (2.158 * 10-9 m3/s) / (1.021 * 10-6 m2)
which results in:
v ≈ 0.00211 m/s
So, the velocity of the water flow in the polyethylene tubing at 25°C is approximately 0.00211 m/s.