Chapter 6, Problem 46P

A sluice gate, which controls flow rate in a channel by simply raising or lowering a vertical plate, is commonly used in irrigation systems. A force is exerted on the gate due to the difference between the water heights y₁and y₂and the flow velocities V₁and V₂upstream and downstream from the gate, respectively. Take the width of the sluice gate (into the page) to be it’. Wall shear stresses along the channel walls may be ignored, and for simplicity, we assume steady, uniform flow at locations 1 and 2. Develop a relationship for the force FR acting on the sluice gate as a function of depths y₁and y₂, mass flow rate h, gravitational constant g, gate width w, and water density p.