Homework Assignment #1.
Coverage: Lectures 1 and 2.
Deadline: September 24, 2023
Total worth: 4 points. 50% reduction is in place for late submission. HW Assignment #1 will
not be accepted past MidTerm Exam date.
Submission Method: Handwritten note arranged into one PDF submitted through MS Teams or
e-mail.
File name: HWA1_LastName.pdf
Problem 1 (0.6 points).
Test, for dimensional homogeneity, the following formula for volume flow Q through a hole of
diameter D in the side of a tank whose liquid surface is a distance h above the hole position:
where g is the acceleration of gravity. What are the dimensions of the constant 0.68?
Problem 2 (0.6 points).
A container has 0.9 m3 of Helium stored at pressure of 200 kPa and a temperature of 20°C.
Calculate the mass (kg) of the gas on the surface of
i) The earth
ii) The moon
iii) Calculate the heat transfer (MJ) needed to enlarge the gas isothermally to a volume of
1.5 m3
Problem 3 (0.6 points).
Under the normal conditions a vertical concentric annulus has outer radius R0 and inner radius
Ri, is lowered into fluid of surface tension σ and contact angle θ < 90°. Derive an expression for
the capillary rise h in the annular gap, if the gap is very narrow.
Problem 4 (0.8 points).
Under normal conditions the temperature of the atmosphere decreases with increasing elevation.
In some situations, however, a temperature inversion may exist so that the air temperature
increases with elevation. A series of temperature probes on a mountain give the elevation–
temperature data shown in the table below. If the barometric pressure at the base of the
mountain is 12.1 psia, determine by means of numerical integration the pressure at the top of the
mountain.
Problem 5 (0.6 points).
A U-tube manometer contains oil, mercury, and water as shown in the figure below. For the
column heights indicated what is the pressure differential between pipes A and B?
Problem 6 (0.8 points).
A long, vertical wall separates seawater from fresh water. If the seawater stands at a depth of
7m, what depth of freshwater is required to give a zero resultant force on the wall? When the
resultant force is zero, will the moment due to the fluid forces be zero? Explain.