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  Expt. No.
  
  Date:
  STUDY OF UNIFORM FLOW FORMULAE
  
  Aim: To determine the Chezys constant (C) and the Mannings constant (n) for the given
  channel bed for the uniform flow.
  Theory: An open channel flow is said to be uniform if the flow characteristics like velocity,
  depth, slope and c/s remains constant for a given length of channel. Consider section 1-1 and 2-2
  as shown in the figure, the forces acting on the water between the sections considered are:
  1. The component of the wt. of water in the direction of the flow (ALsin
  2. The frictional resistance against the flow of water (fPLV2)
  3. Pressure forces at the section 1-1.
  4. Pressure forces at the section 2-2.
  Where L=length of channel;
  A=Area of flow of water;
  S=slope of bed;
  V=mean velocity of flow;
  f=frictional resistance;
  P=wetted perimeter.
  As the depth of the water at the section 1-1 & 2-2 are the same the pressure forces on these two
  sections are same and acting in the opposite direction. Hence they cancel each other. In case of
  the uniform flow, the velocity does not change along the length of the channel, thus there is no
  acceleration acting on water. Hence the sum of the component of all the external forces in the
  direction of the flow must be equal to zero. In short, for this uniform flow to exist the driving
  forces (due to gravity) should be equal to the resisting force (due to the friction forces).
  ALsin - fPLV2 = 0
  V2 =( Asin )/ fP
  V=
  
  fP
  Asin)/
  
  V=C RS
  Where R=A/P =hydraulic depth or hydraulic radius.
  C= /f = chezys constant and for small values of ; tan = sin = 0
  
  Therefore, chezys constant = C = V/ RS
  
  And Mannings constant = n = (R2/3 S1/2) / V
  Experimental set up : It consists of glass walled (Perspex sheet made) rectangular tilting bed
  flume 5m long , 10.3 cm wide and 60 cm deep into which water is supplied by a pump. A sluice
  is fitted in the upstream side of the flume. A pointer gauge is used to measure the depth of water
  in the channel.
  Procedure:
  1. A channel bed of tilting is adjusted to certain slope by adjusting the jack.
  2. Two or more different section may be chosen. Pointer gauge readings for the bed level
  these sections are taken.
  3. Water is supplied to the flume by starting the pump. Discharge is adjusted to get the
  suitable value of the depth of flow in the flume.
  4. After waiting for some time the flow becomes uniform. Then the pointer gauge readings
  for the top surface of the water is taken.
  5. The water is collected in the discharge tank and rate of flow of water is measured.
  6. Steps 2 to 5 are repeated for other values of discharge.
  
  Observations:
  i.
  ii.
  iii.
  
  Area of collection tank = a =
  
  Width of the channel = B =
  Initial bed reading of the flume:
  a. At section 1-1 = h1 =
  b. At section 2-2 = h2 =
  
  Sr.
  No.
  
  Slope
  S
  
  Section 1-1
  H1 (cm)
  
  Section 2-2
  H2 (cm)
  
  Height of water
  collected in
  tank h (cm)
  
  Time to collect the
  
  water in the tank
  t (sec)
  
  Observation table :Table 2
  
  Slope
  
  Depth of flow
  
  Y1=
  H1-h1
  (cm)
  
  Y2=
  H2-h2
  (cm)
  
  Y=
  Y 1 +Y 2
  2
  (cm)
  
  Formulae:
  1.
  
  Y=
  
  Y 1 +Y 2
  2
  
  2. A= B Y
  3. P= B+2Y
  4. R= A/P
  
  5. Qexpt. =
  
  6. V =
  
  a h
  t
  
  Q expt .
  A
  
  A=
  BY
  (m2)
  
  P=
  B+2Y
  (m)
  
  R=
  A/P
  (m)
  
  Qexpt.
  V=
  3
  Q/A
  (m /sec)
  (m/sec)
  
  Chezys
  
  Mannings
  
  7. C = V/ RS
  8. n = (R2/3 S1/2) / V