A gas flows with a velocity v along a pipe of...

A gas flows with a velocity $v$ along a pipe of cross-sectional area $S$ and bent an angle of $90^{\circ}$ at a point $A .$ What force does the gas exert on the pipe at $A$ if its density is $\rho$ ? (a) $\frac{\sqrt{2} S v}{\rho}$ (b) $\sqrt{2} S v^{2} \rho$ (c) $\frac{\sqrt{3} S v^{2} \rho}{2}$ (d) $\sqrt{3} S v^{2} \rho$

A gas flows with a velocity $v$ along a pipe of cross-sectional area $S$ and bent an angle of $90^{\circ}$ at a point $A .$ What force does the gas exert on the pipe at $A$ if its density is $\rho$ ?
(a) $\frac{\sqrt{2} S v}{\rho}$
(b) $\sqrt{2} S v^{2} \rho$
(c) $\frac{\sqrt{3} S v^{2} \rho}{2}$
(d) $\sqrt{3} S v^{2} \rho$

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Key Concepts

Mass Flow Rate

Mass flow rate is the amount of mass passing through a given cross-sectional area per unit time, calculated as the product of the fluid density, cross-sectional area, and velocity. This concept is essential for determining how much momentum is being transported in a fluid flow.

Momentum Flux

Momentum flux represents the rate at which momentum is carried by the fluid across a surface. It is typically expressed as the product of mass flow rate and velocity, linking the properties of the fluid flow directly to the forces that develop in the system.

Change in Momentum

Change in momentum refers to the variation in the momentum vector of a fluid as it changes direction or speed. In situations such as a bend in a pipe, the fluid undergoes a directional change, and the resulting difference in momentum per unit time gives rise to a force exerted on the boundaries of the flow channel.

Newton's Second Law in Fluid Dynamics

Newton's Second Law, when applied to fluid flow, states that the net force on a system is equal to the rate of change of momentum of the fluid. This principle allows for the calculation of forces acting on structures like pipe bends based on the momentum flux and the change in direction of the fluid flow.

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