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# in a turbulent pipe flow the boundary is hydrodynamically smooth if

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## Hydrodynamically Smooth And Rough Boundaries Assignment help

When the average depth k of the surface irregularities is less than laminar sub-layer of the surface Î´ is called as hydrodynamic ally smooth boundary. Hydrodynamically smooth and rough boundaries assignment help, hydrodynamically smooth and rough boundaries homework help.

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## Hydrodynamically Smooth And Rough Boundaries

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## Hydrodynamically Smooth and Rough Boundaries •    When the average depth  k of the surface irregularities is less than laminar sub-layer of the surface δ is called as hydrodynamic ally smooth boundary.

•    The eddy which formed outside of the laminar sub-layer try to penetrate in the laminar sub-layer boundary is called as smooth boundary as shown in

•    When the average depth k of the surface irregularities is greater than laminar sub-layer of surface δ is called as hydrodynamic ally rough boundary.

•    The eddy which formed outside of the laminar sub layer penetrates into the laminar sub-layer. Such boundary is called as rough boundary as shown in.

(1)    When k / δ < 0.25 , smooth boundary.

(2)    When k / δ > 6 , rough boundary.

(3)    When 0.25 < k / δ < 6, transition boundary.

In terms of roughness Reynold’s number,

(1)    u.k / v < 4, smooth boundary.

(2)    u.k / v > 100, rough boundary.

(3)    u.k / v lies between 4 to 100, transition boundary.

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## [Solved] A boundary is known as hydrodynamically smooth if:

Concept: Hydro-dynamically smooth: If the average height of irregularities (k) is much lesser than the thickness of the laminar sub-layer (δ), then th Home Fluid Mechanics Boundary Layer Theory Terms Associated with Boundary Layer Boundary Layer Thickness

## A boundary is known as hydrodynamically smooth if:

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Kδ=0.3 Kδ>0.3 Kδ<0.25 Kδ=0.5

## Answer (Detailed Solution Below)

Option 3 : Kδ<0.25 Crack with

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## Detailed Solution

Concept:

Hydro-dynamically smooth:

If the average height of irregularities (k) is much lesser than the thickness of the laminar sub-layer (δ), then the boundary is called hydro-dynamically smooth.

Hydro-dynamically rough:

If the average height of irregularities (k) is much greater than the thickness of the laminar sub-layer (δ), then the boundary is called hydro-dynamically rough.

According to NIKURDE's Experiment, the boundary is classified as:

Hydrodynamically smooth when

kδ<0.25

Boundary transition condition, when

0.25

Hydrodynamically rough when

kδ>6

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## More Terms Associated with Boundary Layer Questions

Q1. A block of 2 kg slides on a parallel surface at a speed of 4 m/s. It falls on an unpressed spring and presses it until the block is completely motionless. The amount of kinetic friction is 15 N and the spring constant is 10,000 N/m. Spring presses with _____.Q2. A boundary is known as hydrodynamically smooth if:Q3. A fluid is flowing over a flat plate. At a distance of 8 cm from the leading edge, the Reynolds number is found to be 25600. The thickness of the boundary layer at this point isQ4. What is the ratio of momentum thickness to the boundary layer thickness δ when the layer velocity profile is given by

uU∞=(yδ)1/2

Where u is velocity at height y above surface and

U∞

is free stream velocity of flow.

Q5. 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 _________Q6. 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______.Q7. If U∞ = free stream velocity, u = velocity at y, and δ = boundary layer thickness, then in a boundary layer flow, the momentum thickness θ is given byQ8. The thickness of laminar boundary layer at a distance 'x' from the leading edge over a flat plate varies as:Q9. For laminar flow over a flat plate, the thickness of the boundary layer at a distance from the leading edge is found to be 5 mm. The thickness of the boundary layer at a downstream section, which is at twice the distance of the previous section from the leading edge, will be

## More Boundary Layer Theory Questions

Q1. If the boundary layer over a flat plate, kept parallel to the flow, is laminar. Determine the ratio of the skin-skin friction drags on the front half of the plate to the rear half.Q2. Which condition in the following defines a wall (y = 0) in a boundary layer?Q3. If

B=dydx

Pressure increase along the flow when ________

Q4. When a solid body is immersed in a flowing fluid, there is a narrow region of the fluid in the neighbourhood of the solid, where the velocity of fluid varies from zero to free stream velocity is known as:Q5. According to the boundary layer theory, the flow of fluid in the neighbourhood of the solid boundary may be divided into _______.Q6. Within the boundary layer region, which force dominates over inertia force?

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## Hydro

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Hydro-dynamically smooth and rough boundaries

written 3.6 years ago by

teamques10 ★ 34k

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written 3.6 years ago by

teamques10 ★ 34k (a) Smooth Boundary (b) Rough Boundary

Let the average height of the irregularities projecting from the surface of boundary be denoted as ‘K’.

Now, if the value of ‘K’ is large for a boundary then the boundary is called as Rough boundary.

And if the value of ‘K’ is smaller or less, then the boundary is known as Smooth boundary.

This is the classification of rough and smooth boundaries based on boundary characteristics. But for proper classification flow and fluid characteristics are also considered.

Hydro-dynamically smooth boundary

1) For a turbulent flow analysis, the flow is divided into two parts or portions.

2) The first portion consists of a thin layer of fluid in the immediate neighbourhood of the boundary, where the viscous shear stress is stronger whereas the shear stress due to turbulent is negligible. This is known as laminar sublayer.

3) The second portion of flow is the one where shear stress due to turbulence is higher or large as compared to the viscous shear and this zone is called as Turbulent zone.

4) The zone upto which or the height upto which the effect of viscosity predominates is denoted by

δ ′ δ′ .

5) So, we can say that if the average velocity height ‘K’ is less than ‘

δ ′ δ′

’, then the boundary is called as Smooth boundary.

6) This happens because, outside the laminar sub-layer the flow is turbulent and eddies of various sizes present in the turbulent flow try to penetrate through the laminar sub-layer, but due to the great thickness of laminar sub-layer the eddies are unable to reach the surface irregularities and so the boundary behaves as smooth boundary.

Hydro-dynamically rough boundary

1) If the Reynolds number of the flow increases, the thickness of laminar sub-layer decreases.

2) If this happens, then the average height ‘K’ of irregularities is above the laminar sub-layer and thus the eddies present will come in contact with irregularities of the surface and lot of energy will be lost.

3) Such a boundary is known as Hydro-dynamically rough boundary.

Conditions from Nikuradse’s experiment:-

1) If ( K ′ δ ′ )<0.25 (K′δ′)<0.25 , (smooth boundary) 2) If ( K ′ δ ′ )>6.0 (K′δ′)>6.0 , (Rough boundary) 3) If 0.25<( K ′ δ ′ )<6.0 0.25<(K′δ′)<6.0

, (boundary is in transition)