CORK INSTITUTE OF TECHNOLOGY
INSTITIÚID TEICNEOLAÍOCHTA CHORCAÍ
Semester 2 Examinations 2011/12
Module Title: Fluid Mechanics
Module Code: MECH7006
School: Mechanical & Process Engineering
Programme Title: Bachelor of Engineering (Honours ) in Mechanical Engineering (DME_2)
Bachelor of Engineering (Honours) in Structural Engineering (DSE_2)
Bachelor of Engineering (Honours) in Biomedical Engineering (DBE_2)
Programme Code: EMECH _8_Y2
External Examiner(s): Mr John J Hayes, Prof Sean Leen, Mr John O’ Mahony, Dr Mark Richardson,
Mr Gary Clerkin, Dr Laoise McNamara
Internal Examiner(s): Mr Paul D O’Sullivan
Instructions: Attempt any three questions. (33 marks each)
Duration: 2 hours
Sitting: Autumn 2012
Requirements for this examination:
Note to Candidates: Please check the Programme Title and the Module Title to ensure that you have received the
correct examination paper.
If in doubt please contact an Invigilator.
Q1 Fluid Statics
a) A sluice gate consists of a quadrant of a circle of radius 1.5m pivoted at its centre O. Its
centre of gravity is at G, as Shown in fig 1. When the water is level with the pivot O,
calculate the magnitude and direction of the resultant force on the gate due to the water
and the turning moment required to open the gate. The width of the gate is 3m and it has a
mass of 6000kg. (14 Marks)
b) Discuss with the aid of sketches Archimedes principle and the relative positions of a floating
bodies centre of gravity, center of pressure and metacentric height under stable and
unstable configurations. (3 Marks)
c) A ship has a displacement of 5000 metric tonnes. The second moment of area of the
waterline section about a fore and aft axis is 12000m4 and the centre of buoyancy is 2m
below the centre of gravity. The radius of gyration is 3.7m. Calculate the period of
oscillation. Sea water has a density of 1025 kgm-3. (16 Marks)
Q2 Fluid Momentum
a) Derive the momentum equation for 2 and 3 dimensional flow along a streamline. Include a
sketch in your answer outlining the different velocity components. (13 marks)
Fig 1: sluice gate
b) Ethanol with a specific gravity of 0.81 enters the reducing bend shown in fig 2 with a
velocity of and a pressure of . The bend is in a horizontal plane. Calculate
the x and y forces required to hold the bend in place. Neglect energy losses in the bend.
c) If the bend was installed in a vertical orientation discuss the impact on the resultant force.
Q3 Fluid Motion and Flow Measurement
a) Derive an expression for the velocity of flow issuing from a pipe of length used to empty a
reservoir when the pipe outlet is a distance below the surface of the water in the reservoir.
Ignore all losses except friction. Use a sketch to define the control volume (6 marks)
b) Describe the principle and operation of an orifice plate meter. Write down the equations
governing the flow through such a meter. Outline why a typical discharge coefficient is
significantly different to unity. (11 Marks)
c) An orifice plate is to be used to measure the velocity of airflow through a 2m diameter duct.
The mean velocity in the duct will not exceed 15 ms-1 and a water tube manometer having a
maximum difference between water levels of 150mm is to be used. Assuming Cd is 0.64
determine a suitable orifice diameter to make full use of the manometer range. Take the
density of air to be 1.2 kgm-3. (16 Marks)
Fig 2: Pipe Bend carrying ethanol
Q4 Behaviour of Real Fluids
a) Derive the Hagen Poiseuille Equation below for a pipe of diameter d.
b) Show how this can lead to an expression for friction factor for laminar flow in
a pipe. (8 marks)
c) Calculate the steady rate at which oil will flow through a steel pipe
100 mm in diameter and 120 m long under a head difference of 5 m.