In: Civil Engineering
heat exchanger has water in the outer conduit and ethylene glycol in the inner. It is desired to have a Reynolds number of 1000 in the inner conduit and 15000 in the outer conduit. The inner conduit is 5mm inside diameter and the outer conduit is 12mm inside diameter. Specify the pressure drop per unit length in the each conduit (Pa/m). The inner conduit has a wall thickness of 0.75 mm.
Ans) Given,
Reynold number for inner conduit (Ri)= 1000
Reynold number for outer conduit (Ro) = 15000
We know, head loss(Hf) = f L V2 / 2gD
where, f = Darcy friction factor
L = length
V= flow velocity
g = acceleration due to gravity
For inner conduit, since Reynold number = 1000 < 2000 , flow is laminar , therefore
f = 64/Ri = 64/1000 = 0.064
Also, Ri = VD/
,
where,
=
dynamic viscosity of ethylene glycol = Ns/m2
Density of ethylene glycol = 1100 kg/m3
=> 1000 = 1100 V (0.005)/ 0.0155
=> V = 2.81 m/s
To determine head loss per unit length put L = 1 m
=> Hf = 0.064 x 1 x 2.812 / (2 x 9.81 x 0.005)
= 5.15 m
Pressure drop = gHf
= 1000 x 9.81 x 5.15
= 50521.5 N/m2
Now, for outer conduit,
Dynamic viscosity of water = 0.001 Ns/m2
15000 = 1000 x V x (0.015 - 0.0075) / 0.001 ( Outer diameter of inner conduit = 5 + 2(0.75) = 7.5 mm )
=> V = 2 m/s
Hf = f L V2 / 2gDo
= 0.064 x 1 x 22 / (2 x 9.81 x 0.0075)
= 1.739 m
= 1000 x 9.81 x 1.1739
= 11516 N/m2