MAAE 2300 D, E, and F: Fluid Mechanics I
Winter 2025
Assignment Problems – Set 2
Problem 1:
Consider a fixed lower plate and an upper plate moving with a
constant velocity V. The two plates confine two immiscible liquids
as shown in the figure below. Derive an expression for the velocity
of the upper layer of Liquid 1 in terms of the moving plate
velocity, V, liquid 2 thickness and viscosity h2 and µ2
respectively, and liquid 1 thickness and viscosity h1 and µ1
respectively. Assume µ2 > µ1 and a linear flow velocity profile
within each liquid. (Ans: ܸ ቆ
ଵ
ഋ ೓
ଵା భ ∙ మ
ഋమ ೓భ
ቇ)
Problem 2:
The glass tube has an inner diameter d and is immersed in water at
an angle θ from the horizontal. Determine the average length L to
which water will rise along the tube due to capillary action. The
surface tension of the water is ϓ and its density is ρ (Ans: ‫= ܮ‬
ସ஌
ఘ௚ௗ sin ఏ
). Assume contact angle of water as zero.
Problem 3:
A rain cloud has an approximate volume of 6.50 mile3 and an average
height, top to bottom, of 350 ft. If a cylindrical container on
the ground 6 ft in diameter collects 2 in of water after the rain
falls out of the cloud, estimate the total weight of rain that
fell from the cloud. 1 mile ≡ 5280 ft (Ans: 28.4 x 109 lb).