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Chapter 6: Problem 29

What fluid property is responsible for the development of the velocity boundary layer? For what kind of fluids will there be no velocity boundary layer on a flat plate?

Short Answer

Expert verified
Answer: The fluid property responsible for the development of the velocity boundary layer is viscosity. Ideal (inviscid) fluids, which possess zero viscosity, experience no velocity boundary layer on a flat plate.

Step by step solution

01

Understanding the velocity boundary layer

Depending on the fluid flow, a velocity boundary layer is a region near a solid object, such as a flat plate, where the velocity of the fluid varies greatly from the free-stream velocity (velocity far from the surface) to zero at the surface. This phenomenon occurs due to fluid viscosity, which leads to the no-slip condition at the surface.
02

Identifying the fluid property

As mentioned earlier, fluid viscosity is the property responsible for the development of the velocity boundary layer. Viscosity (denoted as \(\mu\)) is a measure of a fluid's resistance to flow and deformation. The fluid layers close to the surface experience greater resistance against their motion, leading to the decrease in velocity. This variation in velocity from the surface to the free-stream is known as the velocity boundary layer.
03

Determining the type of fluids with no velocity boundary layer

For a fluid to exhibit no velocity boundary layer on a flat plate, it would have to possess zero viscosity. Fluids with zero viscosity are referred to as ideal fluids or inviscid fluids. These fluids don't experience any internal resistance against their motion, and hence, there's no boundary layer formation on the flat plate. In summary, the fluid property responsible for the development of the velocity boundary layer is viscosity, and ideal (inviscid) fluids have no velocity boundary layer on a flat plate.

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Most popular questions from this chapter

Consider steady, laminar, two-dimensional, incompressible flow with constant properties and a Prandtl number of unity. For a given geometry, is it correct to say that both the average friction and heat transfer coefficients depend on the Reynolds number only?

What is Newtonian fluid? Is water a Newtonian fluid?

Consider a fluid flowing over a flat plate at a constant free stream velocity. The critical Reynolds number is \(5 \times 10^{5}\) and the distance from the leading edge at which the transition from laminar to turbulent flow occurs is \(x_{\mathrm{cr}}=7 \mathrm{ft}\). Determine the characteristic length \(\left(L_{c}\right)\) at which the Reynolds number is \(1 \times 10^{5}\).

Friction coefficient of air flowing over a flat plate is given as \(C_{f}=0.664(V x / \nu)^{-0.5}\), where \(x\) is the location along the plate. Using EES (or other) software, determine the effect of the air velocity \((V)\) on the wall shear stress \(\left(\tau_{w}\right)\) at the plate locations of \(x=0.5 \mathrm{~m}\) and \(1 \mathrm{~m}\). By varying the air velocity from \(0.5\) to \(6 \mathrm{~m} / \mathrm{s}\) with increments of \(0.5 \mathrm{~m} / \mathrm{s}\), plot the wall shear stress as a function of air velocity at \(x=0.5 \mathrm{~m}\) and \(1 \mathrm{~m}\). Evaluate the air properties at \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).

Liquid water at \(15^{\circ} \mathrm{C}\) is flowing over a \(0.3\)-m-wide plate at \(65^{\circ} \mathrm{C}\) a velocity of \(3.0 \mathrm{~m} / \mathrm{s}\). Using EES, Excel, or other comparable software, plot (a) the hydrodynamic boundary layer and \((b)\) the thermal boundary layer as a function of \(x\) on the same graph for the range of \(x=0.0 \mathrm{~m}\) to \(x=x_{\text {cr. }}\) Use a critical Reynolds number of 500,000 .
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