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Chapter 6: Problem 34

What does the friction coefficient represent in flow over a flat plate? How is it related to the drag force acting on the plate?

Short Answer

Expert verified
Answer: The friction coefficient (Cf) is a dimensionless measure of the resistance offered by a flat plate to the fluid flow over it. It is the ratio of the skin friction (shear stress) exerted on the fluid by the plate to the dynamic pressure of the fluid flow. The friction coefficient is used to quantify the friction drag force acting on the flat plate. The higher the friction coefficient, the greater the friction drag force experienced by the plate.

Step by step solution

01

Define the friction coefficient in fluid flow

The friction coefficient, often denoted as Cf, represents the dimensionless measure of the resistance offered by a flat plate to the fluid flow over it. It is the ratio of the skin friction (shear stress) exerted on the fluid by the plate to the dynamic pressure of the fluid flow.
02

Describe the role of friction coefficient in calculating drag force

In fluid flow over a flat plate, there are two types of drag forces: friction drag (also called skin friction drag) and pressure drag. The friction drag is caused due to the viscous interaction between the fluid and the flat plate, while the pressure drag results from the pressure difference on the upstream and downstream sides of the plate. The friction coefficient helps in quantifying the friction drag force acting on the flat plate. The drag force due to friction can be calculated using the following formula: Fd = 0.5 * Cf * 蟻 * U^2 * A Where: - Fd is the friction (skin) drag force - Cf is the friction coefficient - 蟻 (rho) is the fluid density - U is the flow velocity relative to the plate - A is the area of the flat plate in contact with the fluid flow
03

Summarize the relationship between friction coefficient and drag force

In summary, the friction coefficient (Cf) represents the resistance offered by a flat plate to the fluid flow over it, and it is used to quantify the friction drag force acting on the flat plate. The higher the friction coefficient, the greater the friction drag force experienced by the plate.

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Most popular questions from this chapter

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

For steady two-dimensional flow over an isothermal flat plate in the \(x\)-direction, express the boundary conditions for the velocity components \(u\) and \(v\), and the temperature \(T\) at the plate surface and at the edge of the boundary layer.

What is the physical significance of the Prandtl number? Does the value of the Prandtl number depend on the type of flow or the flow geometry? Does the Prandtl number of air change with pressure? Does it change with temperature?

Consider a laminar ideal gas flow over a flat plate, where the local Nusselt number can be expressed as \(\mathrm{Nu}_{x}=0.332 \mathrm{Re}_{x}^{1 / 2} \operatorname{Pr}^{1 / 3}\). Using the expression for the local Nusselt number, show that it can be rewritten in terms of local convection heat transfer coefficient as \(h_{x}=C[V /(x T)]^{m}\), where \(C\) and \(m\) are constants.

For laminar flow over a flat plate the local heat transfer coefficient varies as \(h_{x}=C x^{-0.5}\), where \(x\) is measured from the leading edge of the plate and \(C\) is a constant. Determine the ratio of the average convection heat transfer coefficient over the entire plate of length \(L\) to the local convection heat transfer coefficient at the end of the plate \((x=L)\).
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