Boundary layer theory

The pressure drop in an aeroplane model of size 1/50 of its prototype is 4 N/cm². The model is tested in water. Find the corresponding pressure drop in prototype. Take density of air = 1.24 kg/m³. The viscosity of water is 0.01 poise while the viscosity of air is 0.00018 poise.

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Fluid Mechanics Problem Solution Problem Statement The pressure drop in an aeroplane model of size 1/50 of its prototype is […]

The pressure drop in an aeroplane model of size 1/50 of its prototype is 4 N/cm². The model is tested in water. Find the corresponding pressure drop in prototype. Take density of air = 1.24 kg/m³. The viscosity of water is 0.01 poise while the viscosity of air is 0.00018 poise. Read More »

A spillway model is to be built geometrically similar scale of 1/40 across a flume of 50cm width. The prototype is 20m high and the maximum head on it is expected to be 2m. (a) What height of the model and what head on the model should be used? (b) If the flow over the model at a particular head is 10 lps, what flow per m length of the prototype is expected? (c) If the negative pressure in the model is 150mm, what is the negative pressure in the prototype?

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Fluid Mechanics Problem Solution Problem Statement A spillway model is to be built geometrically similar scale of 1/40 across a

A spillway model is to be built geometrically similar scale of 1/40 across a flume of 50cm width. The prototype is 20m high and the maximum head on it is expected to be 2m. (a) What height of the model and what head on the model should be used? (b) If the flow over the model at a particular head is 10 lps, what flow per m length of the prototype is expected? (c) If the negative pressure in the model is 150mm, what is the negative pressure in the prototype? Read More »

A ship 250m long moves in seawater, whose density is 1030 kg/m³. A 1:125 model of this ship is to be tested in wind tunnel. The velocity of air in the wind tunnel around the model is 20m/s and the resistance of the ship is 50N. Determine the velocity and resistance of the ship in seawater.

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Fluid Mechanics Problem Solution Problem Statement A ship 250m long moves in seawater, whose density is 1030 kg/m³. A 1:125

A ship 250m long moves in seawater, whose density is 1030 kg/m³. A 1:125 model of this ship is to be tested in wind tunnel. The velocity of air in the wind tunnel around the model is 20m/s and the resistance of the ship is 50N. Determine the velocity and resistance of the ship in seawater. Read More »

A pipe of diameter 1.8m is required to transport oil of sp.gr. 0.8 and viscosity 0.04 poise at the rate of 4 m³/s. Tests were conducted on a 20cm diameter pipe using water at 20°C. Find the velocity and rate of flow in the model.

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Fluid Mechanics Problem Solution Problem Statement A pipe of diameter 1.8m is required to transport oil of sp.gr. 0.8 and

A pipe of diameter 1.8m is required to transport oil of sp.gr. 0.8 and viscosity 0.04 poise at the rate of 4 m³/s. Tests were conducted on a 20cm diameter pipe using water at 20°C. Find the velocity and rate of flow in the model. Read More »

Show by dimensional analysis that the power P required to operate a test tunnel is given by P=ρL²V³ϕ(μ/ρLV) where ρ is density of fluid, μ is viscosity, V is fluid mean velocity, P is the power required and L is the characteristics tunnel length.

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Fluid Mechanics Problem Solution Problem Statement Show by dimensional analysis that the power P required to operate a test tunnel

Show by dimensional analysis that the power P required to operate a test tunnel is given by P=ρL²V³ϕ(μ/ρLV) where ρ is density of fluid, μ is viscosity, V is fluid mean velocity, P is the power required and L is the characteristics tunnel length. Read More »

The pressure difference (∆P) in a pipe of diameter (D) and length (L) due to viscous flow depends on the velocity of fluid (V), viscosity (µ) and density (ρ). Using Buckingham’s π theorem, show that ∆P=(µVL)/D² · f(Re) where Re=ρDV/μ is Reynold’s number.

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Fluid Mechanics Problem Solution Problem Statement The pressure difference (∆P) in a pipe of diameter (D) and length (L) due

The pressure difference (∆P) in a pipe of diameter (D) and length (L) due to viscous flow depends on the velocity of fluid (V), viscosity (µ) and density (ρ). Using Buckingham’s π theorem, show that ∆P=(µVL)/D² · f(Re) where Re=ρDV/μ is Reynold’s number. Read More »

If the resistance to motion of a sphere through a fluid (R) is a function of the density (ρ), viscosity (µ) of the fluid, and the radius (r) and velocity (u) of the sphere, develop a relationship of R using Buckingham’s π theorem.

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Fluid Mechanics Problem Solution Problem Statement If the resistance to motion of a sphere through a fluid (R) is a

If the resistance to motion of a sphere through a fluid (R) is a function of the density (ρ), viscosity (µ) of the fluid, and the radius (r) and velocity (u) of the sphere, develop a relationship of R using Buckingham’s π theorem. Read More »

Power input to a propeller (P) is expressed in terms of density of air (ρ), diameter (D), velocity of the air stream (V), rotational speed (ω), viscosity (µ) and speed of sound (C). Show that P=cρω^3 D^5 where c = constant. Use Rayleigh’s method.

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Fluid Mechanics Problem Solution Problem Statement Power input to a propeller (P) is expressed in terms of density of air

Power input to a propeller (P) is expressed in terms of density of air (ρ), diameter (D), velocity of the air stream (V), rotational speed (ω), viscosity (µ) and speed of sound (C). Show that P=cρω^3 D^5 where c = constant. Use Rayleigh’s method. Read More »

Assuming the drag force exerted by a flowing fluid (F) is a function of the density (ρ), viscosity (µ), velocity of fluid (V) and a characteristics length of body (L), show by using Rayleigh’s method that F=CρA V2/2 where A is area and C is constant.

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Fluid Mechanics Problem Solution Problem Statement Assuming the drag force exerted by a flowing fluid (F) is a function of

Assuming the drag force exerted by a flowing fluid (F) is a function of the density (ρ), viscosity (µ), velocity of fluid (V) and a characteristics length of body (L), show by using Rayleigh’s method that F=CρA V2/2 where A is area and C is constant. Read More »

Using Rayleigh’s method, derive an expression for flow through orifice (Q) in terms of density of liquid (ρ), diameter of the orifice (D) and the pressure difference (P).

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Fluid Mechanics Problem Solution Problem Statement Using Rayleigh’s method, derive an expression for flow through orifice (Q) in terms of

Using Rayleigh’s method, derive an expression for flow through orifice (Q) in terms of density of liquid (ρ), diameter of the orifice (D) and the pressure difference (P). Read More »

A kite, which may be assumed to be a flat plate and mass 1kg, soars at an angle to the horizontal. The tension in the string holding the kite is 60N when the wind velocity is 50 km/h horizontally and the angle of string to the horizontal direction is 35°. The density of air is 1.2 kg/m³. Calculate the drag coefficient for the kite in the given position if the lift coefficient in the same position is 0.45. Both coefficients have been based on the full area of the kite.

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Fluid Mechanics Problem Solution Problem Statement A kite, which may be assumed to be a flat plate and mass 1kg,

A kite, which may be assumed to be a flat plate and mass 1kg, soars at an angle to the horizontal. The tension in the string holding the kite is 60N when the wind velocity is 50 km/h horizontally and the angle of string to the horizontal direction is 35°. The density of air is 1.2 kg/m³. Calculate the drag coefficient for the kite in the given position if the lift coefficient in the same position is 0.45. Both coefficients have been based on the full area of the kite. Read More »

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