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Chapter 1: Problem 11

The momentum flux (discussed in Chapter 5) is given by the product \(\dot{m} V\), where \(\dot{m}\) is mass flow rate and \(V\) is velocity. If mass flow rate is given in units of mass per unit time, show that the momentum fux can be expressed in units of force.

Short Answer

Expert verified
The units of both momentum flux and force are kg⋅m/s². Therefore, momentum flux can indeed be expressed in units of force.

Step by step solution

01

Identification of given and unknowns

Identify the given values and the unknowns. The given values are the mass flow rate \(\dot{m}\) (mass per unit time) and the velocity \(V\). The unknown is the units of the momentum flux.
02

Definition and Units of Momentum Flux

Define momentum flux and its units. Momentum flux is defined as the product of mass flow rate and velocity. In terms of units, mass flow rate is typically expressed in kg/s (kilogram per second) and velocity in m/s (metres per second). Thus, the units of momentum flux are kg⋅m/s².
03

Definition and Units of Force

Define force and its units. According to Newton's second law of motion, force is defined as the product of mass and acceleration. Acceleration, in turn, is the rate of change of velocity with time. Therefore, the units of force are also kg⋅m/s².
04

Comparing Units

Compare the units of momentum flux and force. It can be seen that the units of momentum flux \( \dot{m}V \) (kg⋅m/s²) and force (kg⋅m/s²) are the same. Hence, it can be concluded that momentum flux can indeed be expressed in units of force.

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