The application of the linear momentum equation can be used to analyze the forces needed to hold a 180-degree pipe bend in place with flowing water. In this case, water flows through the bend with a constant cross-sectional area of 0.01 square meters and a flow velocity of 15 meters per second. The pressure at the entrance is 0.2 Megapascals and the pressure at the exit is 0.16 Megapascals.
The goal is to determine the force components in the x and y directions to hold the pipe in place. Since the flow is only in the y direction at both the entrance and exit, the force in the x direction is zero. The force component in the y-direction can be calculated by considering the flow behavior across the control volume. The velocity in the y direction is positive at the inflow and negative at the outflow, while the mass flow rate remains constant throughout the bend according to the continuity equation.
By using the mass flow rate and applying the linear momentum equation, the y-component of the anchoring force can be found. This process allows for a clear analysis of the forces acting on the pipe bend due to the flow of water.
Water is flowing through a horizontal, U-shaped pipe bend. The cross-sectional area of the flow is 0.01 square meters, and the magnitude of the flow velocity is 15 meters per second throughout the bend.
The pressure at the entrance is 0.2 Megapascals, and the pressure at the exit is 0.16 Megapascals.
The objective is to find the components of the anchoring force along the x and y directions required to secure the bend in place.
Here, at the entrance and exit, the flow is in the y direction alone, indicating that the magnitude along the x direction reduces to zero.
The magnitude of the component force in the y direction can be obtained by simplifying the expression of the control volume.
The y-component of velocity is positive at the inflow and negative at the outflow, while the mass flow rate is negative at the inflow and positive at the outflow. According to the continuity equation, the mass flow can be considered constant.
With the expression of mass flow, the component of force in the y direction can be obtained.
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