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In incompressible fluid flows over a flat plate with zero pressure gradient. The boundary layer thickness is 1 mm at a location where the Reynolds number is 1000. If the velocity of the fluid alone is increased by a factor of 4, then the boundary layer thickness at the same location, in mm, will be

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  1. 0.5
  2. 2
  3. 0.25
  4. 4

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Option 1 : 0.5
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Explanation:

Boundary Layer Thickness in Incompressible Flow

Definition: In fluid dynamics, the boundary layer is the thin region adjacent to a solid surface where the effects of viscosity are significant. For incompressible flow over a flat plate with zero pressure gradient, the boundary layer thickness depends on the Reynolds number and the velocity of the fluid. The Reynolds number (Re) is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in the flow.

For laminar flow over a flat plate with zero pressure gradient, boundary layer thickness is inversely proportional to the square root of the Reynolds number, i.e.,

Calculation:

Given:

Initial Reynolds number,

Initial boundary layer thickness,

Velocity increased by a factor of 4 ⇒

Reynolds number is directly proportional to velocity, so

Now,

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Q2.The velocity distribution in the boundary layer is given by \(\rm \frac{u}{U} = {\left( {\frac{y}{δ}} \right)^{1/7}}\) \(\rm \left[ \begin{array}{l} u = \rm po{\mathop{\rm int}}\space velocity\space at\space distance\space y\\ \rm U = \rm free\space stream\space velocity\\ \rm δ = nominal\space thickness \end{array} \right]\) What would be the displacement thickness(δ*)?
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Q8.A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Assuming kinematic viscosity, v = 30 × 10-6 m2/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is _________
Q9.The ratio of the thickness of the thermal boundary layer to the thickness of the hydrodynamic boundary layer is equal to (Prandtl number)n, where n is______.

More Boundary Layer Theory Questions

Q1.The Moody chart, a logarithmic chart between frction factor and _________ for a variety of relative roughness in a pipe flow.
Q2.As compared to laminar flow, the boundary layers in a turbulent flow will be:
Q3.When wind is blowing over a reservoir, a boundary layer will develop. 
Q4.The concept of boundary layer was first introduced by
Q5.In the boundary layer, the flow is: 
Q6.The thickness of laminar sub layer 'd' is given by (with usual notations)
Q7.It is known as the _______ distance at which the whole loss of momentum per second would be equivalent to passing through a stationary plate.
Q8.The velocity distribution in the boundary layer is given by \(\rm \frac{u}{U} = {\left( {\frac{y}{δ}} \right)^{1/7}}\) \(\rm \left[ \begin{array}{l} u = \rm po{\mathop{\rm int}}\space velocity\space at\space distance\space y\\ \rm U = \rm free\space stream\space velocity\\ \rm δ = nominal\space thickness \end{array} \right]\) What would be the displacement thickness(δ*)?
Q9.A plate of 500 mm × 200 mm has been placed longitudinally in a stream of an oil which flows with a velocity of 1.0 m/s. The kinematic viscosity of the oil was 0.5 stoke. The thickness of the boundary layer at the trailing edge is _______.
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