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Mecanica de fluidos

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1.
The velocity profile within a laminar boundary layer on a flat plate is given approximately by u/
=
where
is the local boundary layer thickness given by
(
)
, where
is the velocity far from the plate, and the srcin is located at the leading edge of the plate. How does the wall shear stress vary with x? If the fluid is at 20°C and
=30m/s, estimate the grag on one side plate 2m wide by 3 m long. 2.
At 5Kg cube 12 cm on a side slides down an oil-coated incline. If the incline makes a 10° angle with the horizontal and the oil layer is 0.2 00 trick, estimate the speed with which the block slides down the incline. Ignore end effects and assume a linear velocity profile in the oil layer. The viscosity of the oil is 0.1 Pa-s. 3.
The height h of the water in the glass tube shown is 50mm. The diameter of the tube is 2.5 mm. what would the height in the tube be if the surface tension of the water were zero? To what height would the water rise if the tube were 1.0 mm in the diameter? For each tube, what would the percentage error be in the height measurement if the capillary effect were not taken into account? Let the water temperature be 20°C.
4.
A soap bubble hangs from a horizontal circular ring of radius equal to 3 cm: The mass of the soapy water comprising the bubble is 0.0014 kg. Assuming the bubble is spherical and neglecting any contact angle effects at the junction of the ring and the bubble. A] Find t
he angle, θ,
between a tangent to the bubble at the ring and the vertical if the surface tension of the soapy water is 0.05 N/m. Assume the acceleration due to gravity is 9.8 m/s2. [B] Find the radius of the soap bubble. [C] Find the thickness of the soap bubble given that the density of the soapy water is 1000 kg/m3. [D] Could you devise a way to measure surface tension liquid with arrangement?. What would you measure? 5.
A plane wall is immersed in a large body of liquid of density ρ which is at rest:
The surface tension of the liquid surface is denoted by S and the contact angle with the
wall by θ. Find the equation of the water surface in the form y = y(x) ; the function should contain the quantities S, θ, ρ and the acceleration due to gravity, g. To simplify the
problem assume that the curvature of the water surface can be approximated by
.
Find the height, h, in terms of S, θ, ρ and g.

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