FLUID MECHANICS FUNDAMENTALS+APPS
4th Edition
ISBN: 2810022150991
Author: CENGEL
Publisher: MCG
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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.
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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 ? .
Two branches of water pipe merge to form a larger diameter as shown figure below. At a location at the junction (before completely merging) the nonuniform profile is observed at the depth of 6 ftDetermine the value of V (ft / s) .
The figure shows a channel with width of 2.4 m. The density of the water is 1000 kg/m^3. The flow is steady. At the entrance of the channel, the flow is uniform with
velocity V (m/s) while at the exit, the flow has developed the shown velocity profile u(y) = 4y-2y^2 (m/s) and y is in (m). Answer the following questions.
The area in (m^2) of the entrance is:
V
0.75
u = 4y – 2y?
The area in m^2 at the exit section is:
The average velocity in (m/s) at the exit section is:
Chapter 6 Solutions
FLUID MECHANICS FUNDAMENTALS+APPS
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