ES2C5
THE UNIVERSITY OF WARWICK
Second Year Mock Examination: 2018/19
DYNAMICS AND FLUID MECHANICS
Candidates should answer All FOUR QUESTIONS.
Time Allowed : 2 hours.
Only calculators that conform to the list of models approved by the School of Engineering may
be used in this examination. The Engineering Databook and standard graph paper will be
provided.
Read carefully the instructions on the answer book and make sure that the particulars required are
entered on each answer book.
USE A SEPARATE ANSWER BOOK FOR EACH SECTION
, ____________________________________________________________________
SECTION A : FLUID DYNAMICS
________________________________________________________________________________
1.
(a) Calculate the minimum flight speed 𝑈 of an aircraft flying at constant altitude. Consider an
aircraft with maximum take-off mass 𝑚 = 30,740 kg, a lift coefficient 𝐶- = 1.2 and a total
lifting surface of 𝐴 = 140 m3 . Assume that the cruising altitude is 10 km where the
density of air is 𝜌 = 0.414 kgm56 and the acceleration due to gravity is 𝑔 = 9.776 ms 53 .
(6 marks)
(b) Water of density 𝜌 = 998 kgm56 flows steadily through a piping junction with a
showerhead (S) of diameter 𝑑= = 4 cm as illustrated in Fig. Q1b. The cross-sectional
areas, 𝐴? = 𝐴3 and 𝐴6 of sections (1), (2) and (3) have diameters as identified in Fig. Q1b.
The water enters section (1) with a volumetric flow rate of 𝑞? = 75 litres per minute. The
average flow velocity in section (2) is 𝑣3 = 2.5 ms 5? . A portion of the flow is diverted
through section (3) to the showerhead at (S). The showerhead contains 100 holes of
diameter 𝑑C = 1 mm. Assuming uniform shower flow, estimate the exit velocity, 𝑣C , of
the jets ejecting from the holes in the showerhead.
Fig. Q1b: Flow through piping junction with showerhead.
(10 marks)
(c) A circular cylinder is placed in an air flow as shown in Fig. Q1c. The free stream flow
velocity upstream of the sphere is u¥ = 40 m s -1 and the pressure in the free stream is
p¥ = 1.013 × 10 5 Pa . Assume that the air behaves as an ideal fluid and that it has a constant
density of r = 1.226 kg m-3 .
1
THE UNIVERSITY OF WARWICK
Second Year Mock Examination: 2018/19
DYNAMICS AND FLUID MECHANICS
Candidates should answer All FOUR QUESTIONS.
Time Allowed : 2 hours.
Only calculators that conform to the list of models approved by the School of Engineering may
be used in this examination. The Engineering Databook and standard graph paper will be
provided.
Read carefully the instructions on the answer book and make sure that the particulars required are
entered on each answer book.
USE A SEPARATE ANSWER BOOK FOR EACH SECTION
, ____________________________________________________________________
SECTION A : FLUID DYNAMICS
________________________________________________________________________________
1.
(a) Calculate the minimum flight speed 𝑈 of an aircraft flying at constant altitude. Consider an
aircraft with maximum take-off mass 𝑚 = 30,740 kg, a lift coefficient 𝐶- = 1.2 and a total
lifting surface of 𝐴 = 140 m3 . Assume that the cruising altitude is 10 km where the
density of air is 𝜌 = 0.414 kgm56 and the acceleration due to gravity is 𝑔 = 9.776 ms 53 .
(6 marks)
(b) Water of density 𝜌 = 998 kgm56 flows steadily through a piping junction with a
showerhead (S) of diameter 𝑑= = 4 cm as illustrated in Fig. Q1b. The cross-sectional
areas, 𝐴? = 𝐴3 and 𝐴6 of sections (1), (2) and (3) have diameters as identified in Fig. Q1b.
The water enters section (1) with a volumetric flow rate of 𝑞? = 75 litres per minute. The
average flow velocity in section (2) is 𝑣3 = 2.5 ms 5? . A portion of the flow is diverted
through section (3) to the showerhead at (S). The showerhead contains 100 holes of
diameter 𝑑C = 1 mm. Assuming uniform shower flow, estimate the exit velocity, 𝑣C , of
the jets ejecting from the holes in the showerhead.
Fig. Q1b: Flow through piping junction with showerhead.
(10 marks)
(c) A circular cylinder is placed in an air flow as shown in Fig. Q1c. The free stream flow
velocity upstream of the sphere is u¥ = 40 m s -1 and the pressure in the free stream is
p¥ = 1.013 × 10 5 Pa . Assume that the air behaves as an ideal fluid and that it has a constant
density of r = 1.226 kg m-3 .
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