Tranquil flow

Three different types of turbulent flow may be obtained in open channels. They are tranquil flow, rapid flow, and critical flow. In tranquil flow the velocity is less than that at which some disturbance, such as a surge wave, will be transmitted, and the flow is influenced by conditions at both the upstream and the downstream end of the channel. In rapid flow, the velocity of the fluid is greater than the velocity of a surge wave and the... 

Similarly it may be shown that, at the critical conditions, the flowrate is a maximum for a given value of the specific energy J. At the critical velocity, (ir/gD) is equal to unity. This dimensionless group is known as the Froude number Fr. For velocities greater than the critical velocity Fr is greater than unity, and vice versa. It may be shown that the velocity with which a small disturbance is transmitted through a liquid in an open channel is equal to the critical velocity, and hence the Froude number is the criterion by which the type of flow, tranquil or rapid, is determined. Tranquil flow occurs when Fr is less than unity and rapid flow when Fr is greater than unity. 

Kindsvater, C.E., Carter, R.W. (1955). Tranquil flow through open-channel constrictions. 

Large-scale recirculation in the radial plane is observed at the turbulent flow boundary at various distances along the flow axis. The flow is surrounded by a stationary medium that is most often air. Fluctuation of turbulence is recorded in the flow a tranquil flow with lower velocity is recorded behind a turbulent vortex, then it is replaced by a turbulent vortex etc. The flow structure is schematically illustrated in Fig. 11.8. 

Instantaneous gas flow velocities U in the flame base vicinity were obtained in [17]. Those measurements revealed low velocities conditioned by the tranquil flow in zones between the large vortices. In the lower part of the jet (at zlvj 10) the characteristic flow velocity was about 20% of the laminar flame velocity in a stoichiometric mixture. However, for z/r 30 and 50, characteristic velocities were recorded. Velocities of the order of 1.2 are in sufficient agreement with the assumption that the non-turbulent average boundary length between large vortices is measured. 

Thus a hydraulic jump can occur provided that the depth of the liquid is less than the critical depth. After the jump the depth will be greater than the critical depth, the flow having changed from rapid to tranquil. 

Plotting Eq. (10.112) will also show that any rate of discharge less than the maximum can occur at two different depths for a given value of specific energy. If the flow is on the upper limb of the curve, it is said to be upper-stage or tranquil if on the lower limb, it is called lower-stage or shooting. 

Table I shows the size ranges and concentrations of the slurries of silica and iron oxide in isoparaffin and water, that were utilized in the tests. From the stirred, baffled reservoir tank, which was approximately the same volume as the columns, slurry was pumped with a diaphragm pump, using a tranquilizer to even out the flow, into the bottom of the 12.7 cm column, and above the distributor for the 30.5 cm column. In the 12.7 cm column, therefore, slurry passed with the gas through the distributor plate for V- >0. At the top of the column, the slurry was separated from the gas, and returned by gravity to either the reservoir tank, or to a calibrated volume used for slurry flow measurement.

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