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Fluid mechanics problem..?
Water at 10°C (kinematic viscosity = 1.31 x 10-6 m2/s) is to flow from reservoir A to reservoir B through a cast iron pipe (equivalent roughness ∈ = 0.26mm) with a total length of 20m at a target flow rate of 0.002 m3/s. The system contains a sharp edged entrance from reservoir A, six 90° threaded elbows and a sharp enlargement into reservoir B. Reservoir A is elevated 2m higher than of reservoir B. Determine whether 40mm, 45mm or 50mm is the most appropriate internal diameter for the pipe.
well , it is kinda long , and i will not give you numbers but i will show you how to solve it ,
first we are going to use Bernoulli's equation to solve this problem and considering two points, point 1 in which the point of fluid enter from reservoir A to the pipe and point 2 in which the point of fluid gets out from the pipe to reservoir B.
(P1/pg) + (V1^2/2g)+Z1= (P2/pg) + (V2^2/2g)+Z2 + fl/d (V2^2/2g) + SUM( K losses (V2^2/2g) )
where P1= pressure at point 1= atmospheric pressure = zero gauge pressure
V1= velocity at point 1= assume = zero
p= density of fluid (at 10 c = 283 kelvin and get it from water physical properties table )
g= gravity = 9.8 m/s^2
Z1= elevation of point 1= 2m in our case
f= friction factor ( it is a function of two values ∈ /D , Reynold number) Re= (1000*V*d / v)
where V=velocity, d= diameter of pipe, v= kinematic viscosity in mm2/sec = 1.31 mm2/sec in our case and also here :
Re will be a function of V as Re= func.(Velocity).
so you should get f (friction factor ) from a moody chart like the one at the next link :
http://www.thermexcel.com/english/formules/moody.gif
l= length of pipe
d= diameter of pipe
K= loss coefficient ( at entrance and at elbows and at exit)
for this problem , it has been stated that :
sharp edged entrance so consider K entrance= 0.5 and at 90 degree elbows , K = 1.5 and consider at exit K= 1.
so you can find at last that all variables at Bernoulli's equation are available but the Velocity of exit V2
and also Re number is also a function at the Velocity
and also you have Q= flow rate = velocity * area
and by trial and error , at the end you should get the answer.
i am sorry that my answer is short but your question may need 4 or 5 pages to answer 
good luck
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