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Chapter 6: Problem 49

Is the acceleration of a fluid particle necessarily zero in steady flow? Explain.

Short Answer

Expert verified
Answer: No, the acceleration of a fluid particle is not necessarily zero in steady flow. Although the velocity at a particular point remains constant over time, the fluid particle can still experience acceleration due to changes in its velocity vector while moving along the flow path.

Step by step solution

01

Definition of Steady Flow

Steady flow is a flow in which the velocity of the fluid particles at a particular point does not change over time. Mathematically, this can be represented as: ∂v/∂t = 0, where v is the flow velocity and t is the time.
02

Fluid Particle Acceleration

The acceleration of a fluid particle is the rate of change in velocity vector with respect to time. It is given by the equation: a = dv/dt, where a is the acceleration, v is the velocity, and t is the time.
03

Relation Between Steady Flow and Fluid Particle Acceleration

Now, let's analyze whether the acceleration of a fluid particle is zero in steady flow. In steady flow, the velocity of the fluid particle at a point remains constant over time, implying that the rate of change of velocity with respect to time is zero. This doesn't necessarily mean that the fluid particle has zero acceleration because even though the velocity may be constant at a particular point, the fluid particle can still have varying velocities as it moves along the flow path. This results in a non-zero acceleration due to change in velocity vector while the fluid particle is moving along the flow path.
04

Conclusion

In conclusion, the acceleration of a fluid particle is not necessarily zero in steady flow. Even though the velocity at a particular point remains constant over time, the fluid particle can still experience acceleration as its velocity vector changes while moving along the flow path.

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Most popular questions from this chapter

A metal plate \(\left(k=180 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \rho=2800 \mathrm{~kg} / \mathrm{m}^{3}\right.\), and \(\left.c_{p}=880 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) with a thickness of \(1 \mathrm{~cm}\) is being cooled by air at \(5^{\circ} \mathrm{C}\) with a convection heat transfer coefficient of \(30 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If the initial temperature of the plate is \(300^{\circ} \mathrm{C}\), determine the plate temperature gradient at the surface after 2 minutes of cooling. Hint: Use the lumped system analysis to calculate the plate surface temperature. Make sure to verify the application of this method to this problem.

Air at \(5^{\circ} \mathrm{C}\), with a convection heat transfer coefficient of \(30 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), is used for cooling metal plates coming out of a heat treatment oven at an initial temperature of \(300^{\circ} \mathrm{C}\). The plates \((k=180 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), \(\rho=2800 \mathrm{~kg} / \mathrm{m}^{3}\), and \(c_{p}=880 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\) ) have a thickness of \(10 \mathrm{~mm}\). Using EES (or other) software, determine the effect of cooling time on the temperature gradient in the metal plates at the surface. By varying the cooling time from 0 to \(3000 \mathrm{~s}\), plot the temperature gradient in the plates at the surface as a function of cooling time. Hint: Use the lumped system analysis to calculate the plate surface temperature. Make sure to verify the application of this method to this problem.

An average man has a body surface area of \(1.8 \mathrm{~m}^{2}\) and a skin temperature of \(33^{\circ} \mathrm{C}\). The convection heat transfer coefficient for a clothed person walking in still air is expressed as \(h=8.6 V^{0.53}\) for \(0.5

How does turbulent flow differ from laminar flow? For which flow is the heat transfer coefficient higher?

Consider steady, laminar, two-dimensional flow over an isothermal plate. Does the wall shear stress increase, decrease, or remain constant with distance from the leading edge?
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