A long solid cylinder of radius 2 ft hinged at point A is...

Name: Problem 9, Chapter 11: Fundamentals of Thermal-Fluid Sciences
Uploaded: 2022-04-07T16:26:40-08:00
Duration: 5 min 6 s
Channel: Hunza Gilgit
Description: A long solid cylinder of radius 2 ft hinged at point A is used as an automatic gate, as shown in the figure. When the water level reaches 15 ft, the cylindrical gate opens by turning about the hinge at point A. Determine (a) the hydrostatic force acting on the cylinder and its line of action when the gate opens and (b) the weight of the cylinder per ft length of the cylinder

A long solid cylinder of radius 2 ft hinged at point A is used as an automatic gate, as shown in the figure. When the water level reaches 15 ft, the cylindrical gate opens by turning about the hinge at point A. Determine (a) the hydrostatic force acting on the cylinder and its line of action when the gate opens and (b) the weight of the cylinder per ft length of the cylinder

A long solid cylinder of radius 2 ft hinged at point A
is used as an automatic gate, as shown in the figure. When the
water level reaches 15 ft, the cylindrical gate opens by turning
about the hinge at point A. Determine (a) the hydrostatic force
acting on the cylinder and its line of action when the gate opens
and (b) the weight of the cylinder per ft length of the cylinder

Key Concepts

Hydrostatic Pressure Distribution

In fluids at rest, the pressure increases linearly with depth due to the weight of the overlying fluid. This pressure is given by the expression p = ?g(y ? y0), where ? is the fluid density, g is the gravitational acceleration, and y is the vertical coordinate measured downward from the free surface. This concept is fundamental when analyzing forces on submerged surfaces, as it dictates how pressure varies over the surface area.

Hydrostatic Force on a Submerged Surface

The total force acting on a submerged surface is obtained by integrating the pressure over the entire area of the surface. Because the pressure varies with depth, the force calculation involves determining the contributions from pressure at each differential area element and summing these contributions. This method is essential for evaluating the load on structures like gates, dams, and underwater walls.

Center of Pressure

The line of action of the hydrostatic force, known as the center of pressure, is found by equating the moment of the pressure forces to the moment of the resultant force. Unlike the geometric centroid, the center of pressure usually lies deeper and its exact location is determined by integrating the pressure moment about a reference axis. This concept ensures that the torque produced by the distributed pressure is accurately represented by the resultant force acting at the center of pressure.

Weight per Unit Length

When dealing with elongated structures or bodies of uniform cross section, it is often useful to consider the weight distributed along their length. The weight per unit length is calculated by multiplying the cross-sectional area by the material density and gravitational acceleration, normalized over the length. This parameter is crucial in static and dynamic analyses, particularly when determining the equilibrium or response of structures under combined loading conditions.

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