Fuel oil of dynamic viscosity 0.8kg/ms flows at 110litres/second through a 20cm diametercast iron pipe. The density of the fluid is 850kg/m3.(i) Calculate the Reynolds number of the flow
Question
Fuel oil of dynamic viscosity 0.8kg/ms flows at 110litres/second through a 20cm diametercast iron pipe. The density of the fluid is 850kg/m3.(i) Calculate the Reynolds number of the flow
Solution
To calculate the Reynolds number, we can use the formula:
Re = (ρvD)/μ
where: ρ = density of the fluid = 850 kg/m^3 v = velocity of the fluid D = diameter of the pipe = 20 cm = 0.2 m (converted from cm to m) μ = dynamic viscosity = 0.8 kg/(m*s)
First, we need to find the velocity of the fluid. We know that the flow rate (Q) is 110 litres/second. We can convert this to m^3/s by dividing by 1000 (since 1 m^3 = 1000 litres), so Q = 110/1000 = 0.11 m^3/s.
The velocity (v) can be found using the formula Q = vA, where A is the cross-sectional area of the pipe. The area of a circle is given by πD^2/4, so A = π(0.2)^2/4 = 0.0314 m^2.
Therefore, v = Q/A = 0.11/0.0314 = 3.50 m/s.
Now we can substitute these values into the Reynolds number formula:
Re = (850 * 3.50 * 0.2) / 0.8 = 737.5
So, the Reynolds number of the flow is 737.5.
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