Projected Nappes Subject to Transverse Pressure

Sheets of water discharging freely from straight or curved spillways may be subjected to differential pressure across the faces of the nappe. An analytical solution derived for the two-dimensional problem allows determination of the trajectory in cases in which the initial velocity, angle of projection, and nappe thickness are known. The general equations are derived from the equations of motion in horizontal and vertical directions, and the resulting differential equation can be solved if the effects of surface tension are ignored. It is known that surface tension can safely be omitted in most practical applications. Typical results compare favorably with those from similar equations solved by numerical methods on an electronic computer. The sensitivity of thin nappes to transverse pressure difference suggests that an accurate pressure measuring device can be devised by application of the equations developed. The phenomenon of nappe oscillation that sometimes occurs on long free-flow spillways of dams raised by stressed cables and on crest gates is being studied by consideration of the influence of rapidly varying pressures on nappe profiles.