Hydraulic mean depth (Dm) for a circular pipe of diameter 'D' flowing full is 0.25 D. For a circular channel, at Dm = 0.3 D, gives the condition for the maximum
A. Flow rate
B. Mean velocity
C. Both A & B
D. Neither A nor B
Answer: Option C
Solution (By Examveda Team)
Hydraulic mean depth (Dm) is defined as the cross-sectional area of flow divided by the wetted perimeter.For a circular pipe flowing full, Dm = 0.25 D, where D is the diameter of the pipe.
For a circular channel flowing partially, when Dm = 0.3 D, it represents the condition for maximum efficiency of flow.
At this condition, both the flow rate and the mean velocity are maximized, because the hydraulic radius is at its optimum value.
Therefore, the correct answer is Option C: Both A & B
This Question Belongs to Chemical Engineering >> Fluid Mechanics
The correct answer is: C. Both A & B
β Explanation:
Hydraulic mean depth (also called hydraulic radius,
π·
π
=
π΄
π
D
m
β
=
P
A
β
, where
π΄
A = flow area and
π
P = wetted perimeter) plays a key role in determining:
Mean velocity of flow (via Manningβs or Chezyβs equations)
Flow rate (Q), since
π
=
π΄
β
π
Q=Aβ V
π For a circular pipe:
When flowing full,
π·
π
=
π΄
π
=
π
π·
2
/
4
π
π·
=
π·
4
=
0.25
π·
D
m
β
=
P
A
β
=
ΟD
ΟD
2
/4
β
=
4
D
β
=0.25D
For maximum flow/velocity, a circular channel does not flow full.
Instead, the maximum mean velocity and discharge occur when the pipe is flowing about 93% full, corresponding to:
π·
π
β
0.3
π·
D
m
β
β0.3D
This is a well-established hydraulic condition.
β Therefore:
At
π·
π
=
0.3
π·
D
m
β
=0.3D, the circular channel achieves:
Maximum mean velocity
Maximum flow rate
β Final Answer: C. Both A & B