In fluid flow problems, the flow velocity in a long horizontal pipe depends on the pipe...

In fluid flow problems, the flow velocity in a long horizontal pipe depends on the pipe material, pipe geometry and fluid properties in addition to the pump power. For a horizontal pipe with a pump, the friction factor can be obtained from many correlations such as Colebrook-White Equation: 1.1098 :-2 log 3.7065 r) 5.0452 -log Re +5.8506 (Re) -0.8981 -) 2.8257 (1) In which, fis the friction factor and is the roughness ratio given by: given by: PDV Re Where is the roughness of the pipe material and D is the pipe diameter. Note that ruis dimensionless and hence both & and D should be expressed in the same units. Re is Reynolds number which can be calculated from: (2) Where p is the fluid density, u is the fluid viscosity. A cast iron pipe that is 14.64 cm in diameter is 3.435 km long (3435 m). It is to convey octane. The estimated friction factor fis 0.023. a. Determine the velocity of the flow using secant method with an accuracy of 0.001%. By first solving for Re in (1) and then obtaining the required velocity in (2) b. In another part of the same code, Manipulate equation (1) to have f = F(Re) and plot fversus Re for the interval 3000 S Re S 500,000 For octane: p=701 kg/ mp=0.51x10 N.s/m² For cast iron: e=0.025 cm Note: in Python, In(2) is coded log (2) while the logarithm to the base of 10 like log(2) is coded log10(2) Make sure all units are consistent. Save your file as $123456.py where 123456 is your student ID.