Fluid Mechanics for Chemical Engineering (Class 1), Course No.: 24605, Spring 2021
Final Exam on June 14, 2021
Problem #1 (15 pt). The water flow in a circular pipe with a radius (R) of 1 cm is driven by a pressure
gradient. The flow velocity profile (u) is expressed by the equation below. When the magnitude of shear
stress at the inner surface of the circular pipe is – 0.1 N/m2, what is the maximum velocity (umax) of the
water flow in the pipe? The viscosity of water (μ) is 1.0×10-3 kg/m s.
𝑢(𝑟)= 𝑢𝑚𝑎𝑥 [1 −(𝑟
𝑅)2]
Problem #2 (20 pt). When the solid bulb with a cylindrical rod is submerged in the water, the point P
on the cylindrical rod is located on the free surface of the water, as shown in Figure (a) below. When
the solid bulb with the cylindrical rod is submerged in the unknown oil with its density of ρo, the solid
bulb rises and the point P on the rod indicates the height h of 50 cm above the free surface of the oil
(Figure (b)). What is the density (ρo) of the oil?
A total volume (V) of the bulb and the cylindrical rod submerged in the water is V = 0.5 m3. The cross-
sectional area (A) of the cylindrical rod is A = 0.03 m2. The density of water (ρw) is 1,000 kg/m3.
(Hint: Use of the Law of Buoyancy)
Problem #3 (10 pt). The layered fluids (1 meter of water and 3 meter of oil) are held by the vertical
wall. The density of water (ρw) is 1,000 kg/m3 and the specific gravity of the oil is 2. What is the
hydrostatic force on the wall with a width of 1 meter?
