uel 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 (8 marks)(ii) State whether the flow is laminar or turbulent. (1 mark)(iii) Determine the friction factor.

(i) The Reynolds number (Re) is a dimensionless quantity that is used to predict the onset of turbulence in fluid flow. It is defined as the ratio of inertial forces to viscous forces and can be calculated using the formula:

Re = (Density * Velocity * Diameter) / Viscosity

First, we need to convert the given flow rate from litres/second to m^3/second.

1 litre = 0.001 m^3, so 110 litres/second = 0.11 m^3/second.

The velocity (V) of the fluid can be calculated using the formula:

V = Flow rate / Area

The area (A) of the pipe can be calculated using the formula:

A = π * (Diameter/2)^2

Substituting the given diameter of 20 cm (or 0.2 m) into the formula gives:

A = π * (0.2/2)^2 = 0.0314 m^2

Substituting the calculated area and given flow rate into the velocity formula gives:

V = 0.11 m^3/second / 0.0314 m^2 = 3.5 m/second

Substituting the given density of 850 kg/m^3, calculated velocity, given diameter of 0.2 m, and given dynamic viscosity of 0.8 kg/m.s into the Reynolds number formula gives:

Re = (850 kg/m^3 * 3.5 m/second * 0.2 m) / 0.8 kg/m.s = 747.5

(ii) The flow is generally considered to be laminar if the Reynolds number is less than 2000, and turbulent if the Reynolds number is greater than 4000. Since the calculated Reynolds number is 747.5, the flow is laminar.

(iii) For laminar flow, the friction factor (f) can be calculated using the formula:

f = 64 / Re

Substituting the calculated Reynolds number into the formula gives:

f = 64 / 747.5 = 0.0856