Jet/orifice coefficients – definition of coefficient of velocity (Cv) The coefficient of velocity is defined as the ratio of the following quantities for flow through an orifice:
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Aactual velocity of jet at vena contracta to the theoretical velocity
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Barea of jet at vena contracta to the area of orifice
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Cactual discharge through an orifice to the theoretical discharge
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Dratio of actual head to piezometric head
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Esquare of actual velocity to square of theoretical velocity
Answer
Correct Answer: actual velocity of jet at vena contracta to the theoretical velocity
Explanation
Introduction:Orifice flow is characterized by three standard coefficients: coefficient of velocity (Cv), coefficient of contraction (Cc), and coefficient of discharge (Cd). Correct definitions prevent misuse in calculations.
Given Data / Assumptions:
- Sharp-edged orifice with a vena contracta downstream.
- Steady incompressible flow.
- Negligible upstream approach velocity or accounted separately.
Concept / Approach:Cv compares the actual jet speed to the ideal Bernoulli speed at the orifice plane. Cc captures area contraction (A_jet/A_orifice). Cd measures discharge shortfall: Cd = Cc * Cv.
Step-by-Step Solution:1) Compute theoretical velocity: V_th = sqrt(2 * g * H).2) Measure actual velocity at vena contracta: V_act (e.g., via jet range or Pitot).3) Evaluate Cv = V_act / V_th.4) Use Cd = Cc * Cv for discharge calculations.
Verification / Alternative check:Typical sharp-edge values: Cv ~ 0.95–0.99; Cc ~ 0.61–0.64; Cd ~ 0.58–0.64, confirming the relationships.
Why Other Options Are Wrong:
- Cc definition (option b) and Cd definition (option c) are different coefficients.
- Head ratio (option d) and squared ratio (option e) are not standard definitions of Cv.
Common Pitfalls:Using Cd in place of Cv causes underestimation of jet speed; mislocating the measurement point (must be at vena contracta).
Final Answer:actual velocity of jet at vena contracta to the theoretical velocity