Question

# (a) Describe briefly, what the two-bracketed terms in the following Darcy's equation for pressure drop due to frictional losses represent. In your description, explain how both terms may be used

to provide the head loss in fittings as well as that due to the pipe itself. \Delta P=4 f\left(\frac{L}{d}\right)\left(\frac{\rho u^{2}}{2}\right), \text { where the symbols have their usual meanings. } ) Show how Darcy's equation can be modified to give the 'friction head' and how the friction head is combined with Bernoulli's equation to include frictional losses within the energy balance. (c) A spherical particle of 5 mm in diameter and density of 2200 kg m-3 is settling in a stagnant fluid in the Stokes' flow regime. (i) Calculate the viscosity of the fluid if the fluid density is 990 kg m-3 and the particle falls at a terminal velocity of 8 mm s-1.[4 marks] (ii) What is the drag force on the particle at these conditions? (iii) What is the particle drag coefficient at these conditions? (iv) What is the particle acceleration at these conditions?

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