V₁ 6- 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 y1 and y2 and the flow velocities V1 and V2 upstream and downstream from the gate, respectively. Take the width of the sluice gate (into the page) to be w. 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 y1 and y2, mass flow rate m #, gravitational constant g, gate width w, and water density r. y₁ Sluice gate V₂

V₁ 6- 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 y1 and y2 and the flow velocities V1 and V2 upstream and downstream from the gate, respectively. Take the width of the sluice gate (into the page) to be w. 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 y1 and y2, mass flow rate m #, gravitational constant g, gate width w, and water density r. y₁ Sluice gate V₂