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test2 fm yr2020

Test 2- Fluid mechanics-ME21101
Indian Institute of Technology Kharagpur-India
date: 30/10/2020
• Please workout the questions as a team and submit a single answerscript for a team
• Submit the answerscript in .pdf form as a personal message on Microsoft teams as:
team00 test2.pdf. You can replace 00 by your team number 01, 02,... 17 etc.
• There are 4 questions in Part A and all are compulsory- no choice.
• Answers should accompany the question statement, given, find, assumptions made by you
and solution in detail
• Good hand writing/typesetting is preferred
• Just giving some numbers without detailed construction will not be evaluated
• Mention your team number and member names on the first page of the answer script
• Academic integrity is appreciated. Cross-talking with other teams is not permitted
• Answerscripts for evaluation should reach the instructor before 20.00 hrs of 31/10/2020
• Use fundamental principles like the mass continuity, momentum and the energy conservation.
You are welcome to use both the integral and differential analysis- no issue. It is a take
home examination.
• Part B is for experts-which means a bonus grade. Please submit it separately and not
as a team, if you wish. Instructor will take a final call in this matter.
Part A- 4 questions and all are compulsory- no choice
1. A hemispherical vessel (which holds water) of radius R has a small rounded orifice of
area A at the bottom. hShow that the time
to lower
i the liquid level from h1 to
h2 is given by t = A√2g 3 R h1 − h2
− 5 h1 − h2
. Here, g is the accelaration
due to gravity in vertical direction (take the component value). Work it out using the
control volume analysis.
2. A tornado can be idealized as a Rankine vortex with a core of diameter 30 m. The gauge
pressure at a radius of 15 m is −2000 N/m2 (that is, the absolute pressure is 2000 N/m2
below atmospheric).
• Show that the circulation around any circuit surrounding the core is in between
5000 to 6000 m2 /s.
• Such a tornado is moving at a linear speed of 25 m/s relative to the ground. Find
the time required for the gauge pressure to drop from −500 to −2000 N/m2 .
Neglect compressibility effects and assume an air temperature of 25o C, based on that fix
physical properties of air.
Team number:
Please go on to the next page. . .
Fluid mechanics-ME21101
Page 2 of 2
3. Liquid flowing at a fast speed in a wide, horizontal open channel under some conditions
can undergo a hydraulic jump, as shown. For a suitably chosen control volume, the
flow which enters and leaves the jump may be considered uniform with hydrostatic
pressure distribution. Consider water henters the channel from
i D1 = 0.6 m with V1 = 5
m/s. Show that in general, D2 = D1
1 + 8V12 /gD1 − 1 /2. Evaluate the change in
mechanical energy through the hydraulic jump. If heat transfer to the surroundings is
neglizible, determine the change in water temperature through the jump. The channel
is two-dimensional with unit width normal to the page.
4. A continuous belt, passing upward through a chemical bath at speed U0 , picks up a
liquid film of thickness h, density ρ, and viscosity µ. Gravity tends to make the liquid
drain down, but the movement of the belt keeps the liquid from running off completely.
Assume that the flow is fully developed and laminar with zero pressure gradient, and
that the atmosphere produces no shear stress at the outer surface of the film. State
clearly the boundary conditions to be satisfied by the velocity at y = 0 and y = h.
Obtain an expression for the velocity profile in the fully developed state.
Part B- Experts can answer the following question- not mandatory to others
5. Consider a plane flow develops from rest in between two parallel flat plates. The flow is
bounded by two rigid boundaries at y = 0 and y = h. The flow motion in x-direction is
started from rest by suddenly accelerating the lower plate from rest to a steady velocity
U , whereas the upper plate is held stationary. Show that the velocity distribution is
1 −n2 b t
sin nπy
. Here, b = πh2ν , ν is the kinematic
given by u(y, t) = U 1 − hy − 2U
viscosity and t is the time. Make suitable assumptions and show the solution step by
Team number:
End of exam