Sand is discharged from the silo at A at a rate of 50 kg / s with a vertical velocity of 10 m /

step 1 For A we have dP over dt is equal to 3 .75 N. For B we have F sub friction is equal to F sub ext

Sand is discharged from the silo at A at a rate of 50 kg / s...

Sand is discharged from the silo at $A$ at a rate of $50 \mathrm{kg} / \mathrm{s}$ with a vertical velocity of $10 \mathrm{m} / \mathrm{s}$ onto the conveyor belt, which is moving with a constant velocity of $1.5 \mathrm{m} / \mathrm{s}$. If the conveyor system and the sand on it have a total mass of $750 \mathrm{kg}$ and center of mass at point $G,$ determine the horizontal and vertical components of reaction at the pin support $B$ and roller support $A .$ Neglect the thickness of the conveyor.

Key Concepts

Decomposition of Velocity Components

When fluid is discharged at an angle, its velocity has both horizontal and vertical components. Decomposing the velocity into these components lets us isolate the momentum contributions in the direction of interest, such as the force on a wall, ensuring accurate analysis of the impact force derived from only the relevant component of the velocity.

Momentum Flux

Momentum flux is the rate at which momentum is transferred by the fluid through a given area. In fluid mechanics, it is calculated by multiplying the fluid density, the cross?sectional area, and the square of the velocity component in the direction of interest. It is essential for analyzing forces that fluids exert on surfaces when their momentum changes.

Impulse?Momentum Principle

The impulse-momentum principle relates the force exerted on a fluid to the change in its momentum over time. In the context of fluid jets impacting a surface, this principle is applied by equating the force to the rate of change of momentum, which is particularly useful when calculating the impact force from a steadily flowing jet.

Control Volume Analysis

Control volume analysis involves applying the conservation laws of mass and momentum to a defined region in space to assess fluid behavior. This method is pivotal in problems where fluid jets interact with surfaces, as it allows for the examination of momentum fluxes entering and exiting the control volume to determine the resulting forces.

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