Clearly show all assumptions and calculations. Situation: Water flows in a horiz

Question

Clearly show all assumptions and calculations. Situation: Water flows in a horizontal, 2", schedule 40 (D 2.067"-0.0525 [m]), smooth pipe at a flow rate of L/s]. Density and viscosity of water are 1,000 [kg/m3] and 1 [cP]. respectively, at the conditions o the problem. Requirements: Please, determine the following (7 points each): (a) The Reynolds number. (b) The friction factor. (c) The velocity head, in [m]. (d) The pressure drop corresponding to 100-[m] of straight pipe, in [Pa). (e) The pressure drop corresponding to a standard 90° elbow (Le/D-35), in [Pa). () The permanent pressure drop corresponding to an orifice meter with Do/D-0.8, in [Pa].

Explanation / Answer

Diameter of pipe D = 0.0525 m

Area of pipe = (3.14/4) x D x D = (3.14/4) x 0.0525 x 0.0525

A = 0.002164 m2

Volumetric flow rate Q = A x velocity

8 L/s x 1m3/1000 L = 0.002164 m2 x v

v = 3.6968 m/s

Viscosity = 1 cP x 0.001 Pa-s/cP = 0.001 Pa-s

Part a

Reynolds number Re = D x v x density / viscosity

= 0.0525 m x 3.6968 m/s x 1000 kg/m3 / 0.001 Pa-s

= 194082

Re > 4000

Flow is turbulent

Part b

Friction factor for turbulent flow in smooth pipe

f = 0.316 x Re^(-0.25)

= 0.316 x 194082^(-0.25)

= 0.015055

Part C

Velocity head = v^2 / 2g

= (3.6968 m/s)^2 / (2*9.81 m/s2)

= 0.69655 m

Part d

Length L = 100 m

From the Darcy weisbach equation

Head loss hf = ( 4 x f x L x v^2) / (D x 2g)

= (4*0.015055*100m*0.69655m)/(0.0525m)

= 79.897 m

Pressure drop = density x g x hf

= 1000 kg/m3 x 9.81 m/s2 x 79.897 m

= 783795.47 N/m2

= 783.795 kPa

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