Froude Number
Froude Number - Related Videos
09:15
Hydraulic Jumps
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2023
Source: Alexander S Rattner and Mahdi Nabil; Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA When liquid flows along an open channel at high velocity, the flow can become unstable, and slight disturbances can cause the liquid upper surface to transition abruptly to a higher level (Fig. 1a). This sharp increase in the liquid level is called a hydraulic jump. The increase in the liquid level causes a reduction in the average flow velocity.
FAQs
Matching the Froude number preserves the balance between inertial and gravitational effects between the model and the larger system. Engineers therefore use the model to reproduce gravity-dominated behavior rather than simply matching geometric dimensions or velocity. This approach makes observations from laboratory-scale flow experiments more relevant to full-scale hydraulic designs and related engineering decisions.
The Froude number increases when characteristic velocity increases, because velocity appears in the numerator of Fr = U/√(gL). Increasing the representative length has the opposite effect because length appears under the square root in the denominator. Selecting an appropriate length is therefore essential when comparing flows or applying the calculation to differently sized engineering systems.
Values below, near, and above one identify subcritical, critical, and supercritical conditions, respectively. These categories help engineers organize flow behavior according to the relative influence of inertia and gravity. The classification is especially useful when evaluating wave behavior, because moving between these regimes signals a meaningful change in how gravity-related effects compare with the motion of the fluid.
First identify the characteristic velocity U, gravitational acceleration g, and a representative length L for the system being analyzed. Then substitute them into Fr = U/√(gL). The resulting dimensionless value can be compared with one to classify the flow as subcritical, critical, or supercritical, supporting consistent comparisons among engineering flows with different scales or conditions.
In a hydraulic model, engineers select model conditions so the Froude number agrees with that of the larger system. This preserves the relevant inertial-to-gravitational relationship while the experiment is conducted at a smaller scale. Measurements from the model can then inform the analysis and design of hydraulic structures, particularly where flow behavior and wave effects are important.
Naval engineers apply the Froude number when studying ship resistance and wave-making. Matching or comparing values provides a consistent way to relate fluid motion around a model ship to behavior at another scale. The parameter therefore supports experimental assessment of how a vessel interacts with the water and helps organize observations relevant to ship design.
Open-channel flow analysis, hydraulic-structure design, wave-behavior studies, and ship-resistance investigations all use Froude-number reasoning. In each case, the value provides a common basis for judging the relative roles of inertia and gravity. Its dimensionless form also allows engineers to compare systems of different sizes without treating their raw velocities or lengths as directly equivalent.