Experiment No. 5 Coefficient of Velocity: Discussion and Calculation Sheet

Hydrostatic Force and Centre of Pressure

• The magnitude of the total hydrostatic force (F) is given by F = ρgyA, where ρ is the density of the fluid, g is the acceleration due to gravity, y is the depth to the centroid of the immersed surface, and A is the area of the immersed surface.
• The force will act through the centre of pressure (CP) at a distance yp (measured vertically) from point O, where O is the intersection of the plane of the water surface and the plane of the rectangular surface.
• Theoretical determination of yp: yp = y + Ay/I, where y is the distance from O to the centroid (CG) of the immersed surface, I is the 2nd moment of area of the immersed surface about the horizontal axis through CG.

Flow Through an Orifice

• An orifice is an opening with a closed perimeter in the wall of a tank or in a plate normal to the axis of the pipe through which fluid can flow.
• Theoretical discharge (Qt) is given by Qt = A√(2gh), where A is the cross-sectional area of the orifice, g is the acceleration due to gravity, and h is the head of water above the orifice.
• Coefficient of discharge (Cd) is given by Cd = Qa / Qt, where Qa is the actual discharge.
• Coefficient of velocity (Cv) is defined as the actual velocity at vena contracta to the theoretical velocity.
• Coefficient of contraction (Cc) is defined as the area of the jet at vena contracta to the area of the orifice.

Flow Through an External Cylindrical Mouthpiece

• An external cylindrical mouthpiece is an orifice with a small tube attached to it.
• The standard length of a mouthpiece is 3d, where d is the diameter of the orifice.
• Adding a mouthpiece to an orifice increases the discharge and decreases the pressure at vena contracta.
• Theoretical discharge through the mouthpiece is given by Qt = A√(2gh), where A is the cross-sectional area of the mouthpiece.

Flow Over a V-Notch

• A V-notch is a type of weir that gives more accurate flow measurement than other weirs and orifices when the flow is slightly fluctuating.
• The value of Cd (coefficient of discharge) depends on the flow condition (partially or fully contracted).
• The average value of Cd for a 90° V-notch is 0.58.
• The tail water level should remain below the vertex of the notch, and the minimum ventilation below the flow over the notch at the downstream side should be maintained.
• Water head measurement should be made at some distance upstream from the notch, with a minimum distance of 2.5 times the maximum head above the notch.

Experiments and Calculations

• Experiment No. 4: Flow Through an Orifice
  • Objective: To find the value of Cd for the orifice, to plot Qa vs. Qt, and to plot Qa vs. H.
  • Observation and Calculation Sheet: Record observations of head h, actual head H, actual discharge Qa, and theoretical discharge Qt.
• Experiment No. 5: Coefficient of Velocity by the Coordinate Method
  • Objective: To find the value of Cv (coefficient of velocity) and to plot a graph of Qa vs. Qt.
  • Observation and Calculation Sheet: Record observations of head h, actual head H, actual discharge Qa, and theoretical discharge Qt.
• Experiment No. 6: Flow Through an External Cylindrical Mouthpiece
  • Objective: To find the value of Cd for the mouthpiece, to plot Qt vs. Qa, and to plot Qa vs. H.
  • Observation and Calculation Sheet: Record observations of head h, actual head H, actual discharge Qa, and theoretical discharge Qt.
• Experiment No. 7: Flow Over a V-Notch
  • Objective: To find the value of Cd for the V-notch, to plot Qt vs. Qa, and to plot Qa vs. H.
  • Observation and Calculation Sheet: Record observations of water level, water level above vertex, and actual discharge Qa.

Comment on the results obtained, sources of error, etc. related to determining the Coefficient of Velocity using the Coordinate Method. The observation and calculation sheet includes data on orifice diameter, head correction, observed and actual head, vertical velocity, coordinates, theoretical velocity, and more.