Module Code: Module Title:
Time allowed Hours:
Answer FOUR questions: TWO from Section A, TWO from Section B.
Examiner(s): Prof. T. Megaritis and Dr R. Kirby Special Stationery Requirements:
Thermodynamic and Transport Properties of Fluids, GFC Rogers and YR Mayhew. Only School approved calculators are allowed. Use a separate answer book for each section. If you submit answers to more questions than specified, final marks for the examination will be determined using the best marks which satisfy the rubric.
- 1 ___________________________________________________________________________ SECTION A A1. (a) Explain the meaning of the terms: One-Dimensional Fluid Flow, Steady Fluid Flow, and Incompressible Fluid Flow. [15%] Write the Continuity Equation for a steady, one-dimensional flow and define each term in the equation. If the flow is incompressible what is the simplified form of the equation? [20%] A vertical venturi meter carries a liquid of relative density (specific gravity) of 0.8 and has an inlet diameter of 150 mm and a throat diameter of 75 mm. The pressure tapping at the throat of the venturi is 150 mm above the pressure tapping at the inlet of the venturi. The volumetric flow rate through the venturi is 40 l/s. (i) Assuming that the coefficient of discharge of the venturi is 1.00 (neglecting frictional losses), calculate the pressure difference between the inlet and the throat of the venturi. [40%] A vertical U tube mercury manometer is connected to the pressure tappings at the inlet and the throat of the venturi. The tubes above the mercury are full of the liquid flowing through the venturi meter. Calculate the difference between the levels of the mercury in the two sides of the manometer. [25%]
DATA Gravitational acceleration g = 9.81 m/s2 Density of water = 1,000 kg/m3 Density of mercury = 13,600 kg/m3
- 2 ___________________________________________________________________________ A2. (a) One of the forms of Bernoulli’s Equation is given by:
P V2 + + z = constant ρg 2 g
Define each parameter in the equation and state what are the terms ⎛ P V2 ⎞ P V2 , , z and ⎜ ⎜ ρg + 2g + z ⎟ called. ⎟ ρg 2g ⎝ ⎠ [20%] (b) A liquid is discharged from a reservoir to the atmosphere through a sharp edged orifice. Using Bernoulli’s equation show that the theoretical flow rate through the orifice is given by:
Qth = A 2 gh
where A is the area of the orifice and h is the height of liquid above the orifice (i.e. the orifice is located at a depth h below the liquid surface). The reservoir is open to the atmosphere. [25%] (c) Water is discharged from a reservoir to the atmosphere though a sharp edged orifice of 50 mm diameter. The reservoir is open to the atmosphere and the water level is kept at 4.5 m above the orifice. The measured (actual) flow rate of discharged water through the orifice is 0.0115 m3/s. (i) (ii) Determine the discharge coefficient of the orifice. [30%] If the diameter of the formed vena contracta is 40 mm, determine the contraction and velocity coefficients of the orifice. [25%]
DATA Gravitational acceleration g = 9.81 m/s2 Density of water = 1,000 kg/m3
- 3 ___________________________________________________________________________ A3. (a) Using the Moody diagram, shown on page 5, describe and explain the variation of the friction coefficient with the Reynolds number and the surface relative roughness. [25%] Oil is pumped at a rate of 2400 kg/s from a storage tank to a refinery 150 km away through a pipe of 1.25 m inner diameter. The pipe wall roughness is 0.125 mm. The relative density (specific gravity) of the pumped oil is 0.8. Use the Moody diagram to obtain the friction coefficient and then calculate the frictional head loss in the pipe. [45%] A higher oil demand is projected and the...