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Critical Flow

Critical Flow. Critical Flow Characteristics. The specific energy is a minimum for a given discharge The discharge is a maximum for a given specific energy The specific force is a minimum for a given discharge The velocity head is equal to half the hydraulic depth in a channel of small slope

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Critical Flow

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  1. Critical Flow

  2. Critical Flow Characteristics • The specific energy is a minimum for a given discharge • The discharge is a maximum for a given specific energy • The specific force is a minimum for a given discharge • The velocity head is equal to half the hydraulic depth in a channel of small slope • The Froude number is equal to unity • The velocity of flow in a channel of small slope with uniform velocity distribution is equal to the celerity of small gravity waves in shallow water caused by local disturbances (Chow, 1959)

  3. Rectangular Channel, Specific Energy • The depth at which E is minimum is called the critical depth • When , E may be minimum or maximum. For E to be minimum is positive at the depth.

  4. Properties of Critical Flow • Velocity head in critical flow is one half the critical depth • Critical depth is equal to two thirds of the specific energy

  5. Unit discharge • Specific energy for a rectangular channel having hydrostatic pressure distribution and uniform velocity distribution when , and also when • The shape of q-y curve can be obtained by . , Two roots: and • Flow is maximum at because is negative. q-y curve (Chaudhry, 2008)

  6. Specific Force • The specific force, for a rectangular channel is • The maxima and minima for the curve may be determined by taking derivatives and equating with zero. (valid when flow is critical) • is minimum at critical depth ( is positive)

  7. Wave Celerity • The celerity is defined as the wave velocity with respect to the velocity of the medium in which the wave is traveling. • , celerity

  8. Non-Rectangular Channel • A channel built with unvarying cross section and constant bottom slope is called a prismatic channel. Prismatic channel is having nonrectangular cross section (trapezoidal, triangular, circular, parabolic etc.) • For to be minimum, , • Since for rectangular cross section, or , (hydraulic depth) • For a steep channel having non-uniform velocity is velocity head coefficient, and is the slope of the channel bottom

  9. Application of Critical Flow • Several flow measuring devices have been developed utilizing the unique relations between flow depth and discharge. • For a given specific energy discharge is maximum when the flow is critical. • Critical flow may be produced in a channel by raising the channel bottom. Reducing the channel width or by a combination of these measures.

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