steady incompressible flow in pressure conduits

1. LWCE 301 FLUID MECHANICS
CHAPTER NO.8:
STEADY INCOMPRESSIBLE FLOW
IN PRESSURE CONDUITS

2. PRESENTED BY:
 MOIZ AHMED KHAN
 MUHAMMAD AHMED
 ALI HASSAN

3. 8.13 FLUID FRICTION IN NONCIRCULAR
CONDUIT
• CONDUIT:
A channel for conveying water or other fluid.
• In our discussion so far we have been concerned only with
pipe, for a variety of reason conduit cross-sections often deviate
from circular.
• The appropriate characteristic length to use in evaluating head
losses and Reynolds number for noncircular cross-section area is
the hydraulic diameter. The hydraulic diameter is defined as
Dh = 4
𝐶𝑅𝑂𝑆𝑆−𝑆𝐸𝐶𝑇𝐼𝑂𝑁 𝐴𝑅𝐸𝐴
𝑊𝐸𝑇𝑇𝐸𝐷 𝑃𝐸𝑅𝐼𝑀𝐸𝑇𝐸𝑅
(8.13.1)

4. • Use of hydraulic radius: Rh = A/P
Put in eq. (8.13.1)
Dh = 4Rh (8.13.2)
To use the concept of hydraulic diameter, the head lost and Reynolds number is defined as
hL = f
𝐿
𝐷
v2
2𝐺
=
𝑓
4
𝐿
Rh
v2
2𝑔
(8.13.3)
And
R =
𝐷𝑉
𝑣
= (4Rh )V𝜌/μ (8.13.4)
• Relative roughness is 𝜀/4Rh.
• For this two expressions the head losses in noncircular conduits can be estimated.
• This approach gives good results for turbulent flow, but for laminar flow the result are
poor, because in such flow frictional phenomena are caused by viscous action
throughout the body of the fluid, which in turbulent flow the frictional effect is accounted
for largely by the region to the wall; i.e., it depend on the wetted perimeter.

5. 8.14 MINOR LOSSES IN TURBULENT FLOW
• In addition to head loss due to friction, there are always other heads losses due to pipe
expansion and contraction, bends, valves, and other pipe fittings. These losses are
usually known as Minor losses (hLm).
• in case of a long pipe line, the minor losses may be negligible compared to the friction
losses, however, in the case of short pipelines, their contribution may be significant.

6. • Losses caused by
• Fitting, bends, valves, etc.…

7. • Minor in compression to friction losses which are consider major.
• Losses are proportional to – velocity of flow, geometry of device.
hLm = k v2/2g
• The value of “k” is typically provide for various device.
• Energy lost unit “Nm/m” or lbft/lb.
• “K” lost factor has no unit.
• hLm = minor loss.
• V2 = means flow velocity

8. • Whenever the velocity of a flowing stream is altered either in direction or
in magnitude flow, eddy current are set up and a loss of energy in excess
of the pipe friction in that same length created.
• In addition, head loss generally increase with an increase in the
geometric distortion of the flow.
• Though minor losses are usually confined to a very short length of path,
the effect may not disappear for a considerable distance downstream.

9. 8.15 EMPERICAL EQUATION FOR PIPE
FLOW
• Empirical relation which relationship which relate the flow of water in pipe with physical properties
pipes and pressure drop caused by friction.
• It is design and used in water pipe system fluid sprinkle system.
• The empirical formula have been developed, applicable only to specific fluid and condition but very
convenient in the certain range.

10. • The best example of such a formula is that of haze and Williams, applicable only
to the flow of water. This formula is given in the form
V = 0.85CHW Rh
0.63s0.54
Where
Rh = hydraulic radius
S = hL / L, the energy gradient
• The advantage of this formula over the standard pipe-friction is that the
roughness coefficient CHW is not a function of the Reynolds number and trial
solution are therefore elimination. The value of CHW range frim 140 for every
smooth, straight pipe down to 110 for new riveted-steel and vitrified pipe and to
90 or 80 for old and tuberculated pipe.

11. • Another empirical formula
V = 1/nRh
2/3 S1/2
Where
n = roughness coefficient ( vary from 0.009 for smooth brass and glass pipe ).
• The meaning formula applied to about the same flow range as does the Hazen-
William formula.