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Chapter 6 Momentum Analysis of Flow Systems

Solutions Manual for Fluid Mechanics: Fundamentals and Applications by Çengel & Cimbala

CHAPTER 6 MOMENTUM ANALYSIS OF FLOW SYSTEMS

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Chapter 6 Momentum Analysis of Flow Systems Newton’s Laws and Conservation of Momentum

6-1C Solution

We are to express Newton’s three laws.

Analysis Newton’s first law states that “a body at rest remains at rest, and a body in motion remains in motion at the same velocity in a straight path when the netforce acting on it is zero.” Therefore, a body tends to preserve its state or inertia. Newton’s second law states that “the acceleration of a body is proportional to the net force acting on it and is inversely proportional to its mass.” Newton’s third law states “when a body exerts a force on a second body, the second body exerts an equal and opposite force on the first.” Discussion As we shall seein later chapters, the differential equation of fluid motion is based on Newton’s second law.

6-2C Solution

We are to discuss if momentum is a vector, and its direction.

Analysis Since momentum ( mV ) is the product of a vector (velocity) and a scalar (mass), momentum must be a vector that points in the same direction as the velocity vector. Discussion equation. In the general case, wemust solve three components of the linear momentum equation, since it is a vector

6-3C Solution

We are to discuss the conservation of momentum principle.

Analysis The conservation of momentum principle is expressed as “the momentum of a system remains constant when the net force acting on it is zero, and thus the momentum of such systems is conserved”. The momentum of a body remainsconstant if the net force acting on it is zero. Discussion Momentum is not conserved in general, because when we apply a force, the momentum changes.

6-4C Solution

We are to discuss Newton’s second law for rotating bodies.

Analysis Newton’s second law of motion, also called the angular momentum equation, is expressed as “the rate of change of the angular momentum of a body is equal to the nettorque acting it.” For a non-rigid body with zero net torque, the angular momentum remains constant, but the angular velocity changes in accordance with Iω = constant where I is the moment of inertia of the body. Discussion Angular momentum is analogous to linear momentum in this way: Linear momentum does not change unless a force acts on it. Angular momentum does not change unless a torque acts onit.

6-5C Solution

We are to compare the angular momentum of two rotating bodies

Analysis No. The two bodies do not necessarily have the same angular momentum. Two rigid bodies having the same mass and angular speed may have different angular momentums unless they also have the same moment of inertia I. Discussion momentum. The reason why flywheels have most of their mass at the...