Consider a fully developed laminar flow of a fluid through a 8027 m long and 4 cm diamete horizontal and circular pipe. The dynamic density and the viscosity of the fluid are 1252 kg/m³ and 0.3073 kg/(m.s). The velocity profile at a cross-section is given by:
Consider a fully developed laminar flow of a fluid through a 8027 m long and 4 cm diamete horizontal and circular pipe. The dynamic density and the viscosity of the fluid are 1252 kg/m³ and 0.3073 kg/(m.s). The velocity profile at a cross-section is given by:
Chapter2: Loads On Structures
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Consider a fully developed laminar flow of a fluid through 8027 m long and 4 cm diameter
horizontal and circular pipe. The dynamic density and the viscosity of the fluid are 1252 kg/m³ and
0.3073 kg/(m.s). The velocity profile at a cross-section is given by:
u(r)= 6[1 − ( 7 )²]
-
m/s
Where r is the axial distance from the centre and R is the radius of the pipe.
Determine the following:
(i)
(ii)
the maximum velocity at a cross-section of the pipe, Umax
the average velocity at a cross-section of the pipe, Vave
the volume flow rate, Q
(iv)
Reynolds number, Re
(v)
friction factor, f
(vi)
head loss, hi
(vii)
pressure loss, AP
(viii)
pumping power required,
(ix)
for the same pumping power, the percentage decrease of the flow rate if the pipe is
inclined 10° upward (assume the head loss, hò, calculated in part (vi) does not change)
Useful formulae:
64
f
Re
h₂ = f ( =) ( 2² )
2g
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdc321a7-0572-4d50-a9f3-8afbf4260389%2Fcc85c721-2cb0-4bad-b496-f4e2ea4ff65a%2Fdfsmx5k_processed.png&w=3840&q=75)
Transcribed Image Text:6
Consider a fully developed laminar flow of a fluid through 8027 m long and 4 cm diameter
horizontal and circular pipe. The dynamic density and the viscosity of the fluid are 1252 kg/m³ and
0.3073 kg/(m.s). The velocity profile at a cross-section is given by:
u(r)= 6[1 − ( 7 )²]
-
m/s
Where r is the axial distance from the centre and R is the radius of the pipe.
Determine the following:
(i)
(ii)
the maximum velocity at a cross-section of the pipe, Umax
the average velocity at a cross-section of the pipe, Vave
the volume flow rate, Q
(iv)
Reynolds number, Re
(v)
friction factor, f
(vi)
head loss, hi
(vii)
pressure loss, AP
(viii)
pumping power required,
(ix)
for the same pumping power, the percentage decrease of the flow rate if the pipe is
inclined 10° upward (assume the head loss, hò, calculated in part (vi) does not change)
Useful formulae:
64
f
Re
h₂ = f ( =) ( 2² )
2g
=
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