Question

Calculate the Reynolds number for flow in the needle considered in Example 12.8 to verify the assumption that the flow is laminar. Assume that the density of the saline solution is 1025 kg/m³.(v=1.70 m/s, daimeter =0.150×10-3m and n= 1.00×10-3Ns/m²)

Answer 1

Reynolds number (Re) is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It is calculated using the formula:
Re = (ρ * v * d) / η
where:

ρ is the density of the fluid (kg/m^3)
v is the velocity of the fluid (m/s)
d is the diameter of the needle (m)
η is the dynamic viscosity of the fluid (Ns/m^2)

Given:
Density of the saline solution (ρ) = 1025 kg/m^3
Velocity of the fluid (v) = 1.70 m/s
Diameter of the needle (d) = 0.150 x 10^(-3) m
Dynamic viscosity of the fluid (η) = 1.00 x 10^(-3) Ns/m^2
Substitute the values into the formula to calculate the Reynolds number:
Re = (1025 kg/m^3 * 1.70 m/s * 0.150 x 10^(-3) m) / (1.00 x 10^(-3) Ns/m^2)
Re = (1743.75 x 10^(-3)) / (1.00 x 10^(-3))
Re = 1743.75
Therefore, the Reynolds number for flow in the needle is 1743.75. Since the Reynolds number is less than 2300, the flow is considered to be laminar based on this assumption.