Homework 1 - personal.ce.umn.edu

Homework 1
Fluid Mechanics CE 3502 Spring, 2015
Due: Feb 11 , 2015 (9:30am) in homework drop box outside CivE 277.
For full credit, please show all of your calculations and clearly state any assumptions you made.
(1) What is the ratio of the kinematic viscosity of air to that of water at standard pressure and a temperature of 50°C? What
is the ratio of the dynamic viscosity of air to that of water for the same conditions? If you apply the same constant shear
to a thin layer of each fluid (that is, to a thin layer of air at 50°C and to another thin layer of water at 50°C), which will
have the higher shear rate (deformation rate)?
(2) A water bug of mass 1 g is suspended on the surface of a pond by surface
tension (water does not wet the legs). The bug has six legs. If each leg is in
contact with the water over the same length, what is that length? What
assumptions did you have to make to answer that question?
?
(3) Calculate (a) the maximum capillary rise of water between two vertical glass plates spaced 0.15 mm apart and (b) the
minimum capillary drop if the same plates, now spaced 0.20 mm apart, are in mercury. Assume room temperature.
(4) A manometer is used to measure the pressure
difference between points A and B in a pipe as shown.
Water flows in the pipe,and the specific gravity of the
manometer fluid is S = 1.6. The distances and
manometer deflection are indicated on the figure. Find
(a) the pressure differences pA - pB in kPa and (b) the
difference in piezometric head in m.
(5) For the gate shown below, α = 30°, y1 = 0.30 m, and y2
= 2.5 m. Will the gate fall or stay in position under the
action of the hydrostatic and gravity forces if the gate
itself weighs 150 kN and is 1.0 m wide? Assume T =
10°C. Show your calculations to justify your answer.
9.5 cm
1.3 cm
Manometer
Fluid: S = 1.6
(6) The floating platform shown is supported at each of its four corners by a hollow sealed cylinder 1 m in diameter. Each
cylinder weighs 1.5 kN per meter of length. If the length of each cylinder L is as shown in the diagram below, and the
platform floats 0.10 m above the water surface, what is the weight of the floating platform? Assume that the specific
weight of the water (brackish) is 10,000 N/m3. The platform is square in plan view.
Floating platform
Weight = ?
0.1
L = 3m