Test: Orificemeter - Civil Engineering (CE) MCQ

Both venturimeter and orificemeter is used to calculate the rate of flow of liquid flowing through a pipe, they just differs in construction.
Comparison of Venturimeter and Orifacemeter:

where, a₀ = theoretical throat area, a₁ = area at the inlet, h = difference in head, and C_d = coefficient of discharge. 
As energy loss is more in orifice meter, they have higher head losses.

Coefficient of Velocity (C_v):
(i) It is defined as the ratio between the actual velocity of jet at vena-contracta and the theoretical velocity of jet.
(ii) If V is the actual velocity of jet at vena-contracta then,

(iii) The difference between the theoretical and the actual velocities of the jet at vena-contracta is mainly due to friction at the orifice. 
Generally, the value of C_v varies from 0.95 to .99 for different orifices depending upon their size, shape, head, etc.for sharp-edged orifices, the value of C_v is 0.98.

Devices and their uses:

Coefficient of velocity:
It is defined as the ratio of the actual velocity of the jet at veena contracta V to the theoretical velocity V_th.
Experimentally it is determine by using the following relation


where x= Horizontal distance
y= vertical distance
h= constant head water
Generally the value of C_v varies from 0.95 to .99 for different orifices depending upon their size, shape, head etc. for sharp edged orifices the value of C_v is 0.98.

Concept:
Discharge through a circular orifice is given by;

Where, a = Area of orifice
h = Head above the surface
Calculation:
Given,
Discharge through the orifices are same
h₁ = 25 cm, h₂ = 1 m = 100 cm
∵ we know that, 
and, Q₁ = Q₂

Concept:
Orifice meter

• An orifice meter is a thin plate with a centrally located hole is inserted into the flow passage.
• The flow contracts suddenly as the fluid passes through the hole. The flow continues to contract a short distance downstream the hole.
• The region of the smallest cross-section is known as vena contracta, which is developed downstream the orifice. At vena contracta the kinetic energy of the fluid flow is maximum.
• The minimum cross-section in the orifice meter is not orifice diameter but it’s cross-section at vena contracta.

​​Coefficient of contraction (C_c)
Coefficient of contraction (C_c)  is defined as the ratio of the area of cross-section of vena contracta to the area of cross-section of the orifice.
Coefficient of contraction = C_c = A_c / A₀
where A_c = area of vena-contracta,  A₀ = orifice area
Calculation:
Given:
Orifice diameter = 50 mm, diameter at vena contracta = 40 mm

Coefficient of discharge is the ratio of actual discharge to the theoretical discharge.

Coefficient of discharge for various devices are:
⇒ Venturimeter – 0.95 to 0.98
⇒ Orifice meter – 0.62 to 0.65
⇒ Nozzle  – 0.93 to 0.98
∴ The coefficient of discharge for the nozzle meter lies between the venturi meter and the orifice meter.

Coefficient of discharge (C_d): 

• It is the ratio of actual discharge to theoretical discharge.
• As in a pipe, frictional losses are present therefore Qactual will always be less than Qtheoretical.

Its value is always less than 1.

C_d = 0.62 - 0.65 for orifice meter
C_d = 0.95 - 0.98 for venturi meter

Concepts:
The coefficient of discharge (C_d) is the ratio of the actual discharge (Q_a) to theoretical discharge (Q_th) .
The actual discharge is the discharge obtained when all the looses through orifice or pipe flow are considered. While, theoretical discharge is the discharge obtained under ideal conditions i.e. no loss is considered.
The  theoretical discharge is given as:
Q_th = A × V_th
V_th is the theoretical velocity of flow
Calculations:
Given: V_th = 2 m/s; A = 0.4 m²
So, Q_th = 0.4 × 2 = 0.8 m³/s  or 800 l/s
∴ C_d = 400/800
C_d = 0.5
Other important Coefficients:
1. Coefficient of velocity is the ratio of actual velocity to theoretical velocity.
2. Coefficient of contraction is the ratio of cross-section area at vena-contracta to original cross- sectional area.