Fluid Mechanics and ThermodynamicsWeekly Assessed Tutorial Sheets

Tutor Sheets: WATS 1.

The WATS form a collection of weekly homework type problems in the form of out-of-class tutorial sheets.

Each WATS typically comprises of a couple of main questions of which each has around four/five linked supplementary questions. They were developed as part of an LTSN Engineering Mini-Project, funded at the University of Hertfordshire which aimed to develop a set of 'student unique' tutorial sheets to actively encourage and improve student participation within a first year first ‘fluid mechanics and thermodynamics’ module. Please see the accompanying Mini-Project Report “Improving student success and retention through greater participation and tackling student-unique tutorial sheets” for more information.

The WATS cover core Fluid Mechanics and Thermodynamics topics at first year undergraduate level. 11 tutorial sheets and their worked solutions are provided here for you to utilise in your teaching. The variables within each question can be altered so that each student answers the same question but will need to produce a unique solution.

FURTHER INFORMATION

Please see http://tinyurl.com/2wf2lfh to access the WATS Random Factor Generating Wizard.

There are also explanatory videos on how to use the Wizard and how to implement WATS available at http://www.youtube.com/user/MBRBLU#p/u/7/0wgC4wy1cV0 and http://www.youtube.com/user/MBRBLU#p/u/6/MGpueiPHpqk.

For more information on WATS, its use and impact on students please contact Mark Russell, School of Aerospace, Automotive and Design Engineering at University of Hertfordshire.

© University of Hertfordshire 2009 This work is licensed under a Creative Commons Attribution 2.0 License.

Fluid Mechanics and ThermodynamicsWeekly Assessed Tutorial Sheet 1 (WATS 1)

TUTOR SHEET – Data used in the Worked Solution

Q1. A piezometric tube is used to collect data at a particular location in a pipe line. Calculate –

i) the height of the fluid, (m), in the piezometric tube if the fluid has a density of1391 kg/m3 and the pressure is somehow known to be 121426 Pa. (1 mark)

ii) the pressure of the fluid, (Pa), at the location of the piezometric tube, if the fluid has a relative density of 0.59 and the height of fluid in the tube is 0.62 m.

(1 mark)

iii) the specific gravity of the fluid if the pressure is known to be 1.87 Bar and the height of the fluid in the tube was measured at 470 mm. (1 mark)

Q2. 249 litres of red a fluid, relative density = 0.70, and 133 litres of blue fluid of density 2492 kg/m3, are simultaneously tipped into a rectangular based tank. Assuming that the properties of the fluids are such that they are immiscible (i.e. they don’t mix), and that the tank’s base dimensions are 1.80 m x 1.54m calculate i) the mass of the red fluid (kg) (1 mark)ii) the mass of the blue fluid (kg) (1 mark)iii) the pressure gradient in the red fluid (Pa/m) (1 mark)iv) the pressure gradient in the blue fluid. (Pa/m) (1 mark)v) the pressure difference, (Pa), between a point located at 31 % of the depth of the top fluid

and another point at a depth of 35 % of the bottom fluid. Taking account of the depths you need to do this calculation asPtop – Pbottom (2 marks)

Note: For all questions you may assume that the acceleration due to gravity (g) = 9.81m/s2 and that atmospheric pressure is equal to 1.01325 Bar

_______________________________________________________________________________________________WATS 1. Mark Russell (2005)Student number51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire

2

1

WATS 1 Worked solution

This sheet is solved using the data set for student 51.

Q1 is essentially oriented around solving the hydrostatic equation. i.e. –

dPdZ

=−ρg

Separating the differential terms and getting ready to integrate gives –

∫1

2

dP=∫1

2

−ρ gdZ

Where the pressure and location at position 1 and 2 are shown below.

Assuming that density (ρ) and gravity (g) are constants and do not change with height (Z ) gives the following –

∫1

2

dP=−ρg∫1

2

dZ

Hence after integrating this is simply

P2−P1=−ρg(Z2−Z1)

Note that (Z2−Z1)=h i.e. height of fluid in the piezometric tube and assuming that P2 is the atmospheric pressure and we are working in gauge pressure gives –

−P1=−ρ gh which is the same as P1=ρ gh

The rest of the question simply requires us to solve this relationship and using the newly acquired language of the subject and different units applied to the dimensions.

_______________________________________________________________________________________________WATS 1. Mark Russell (2005)Student number51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire

Point A.31% of the top fluid

Point B.35% of the bottom fluid

i) P1=ρ gh therefore h=

P1

ρg which in this case gives

h = 121426/(1391*9.81) = 8.90 m.

ii) relative density = density of fluid / density of water at 4°C

hence rd= ρ

1000 therefore ρ = 0.59 * 1000 = 590 kg/m3.

P1=ρ gh = 590 * 9.81 * 0.62 = 3588 Pa.

iii) Don’t forget specific gravity = relative density and 1 Bar = 105 Pa. and the height should be in meters!

Don’t forget to do the conversions.

P1=ρ gh i.e. ρ=

P1

gh =

1. 87∗105

9 .81∗0 . 470 therefore ρ = 40557 kg/m3.

But I have asked for specific gravity. Hence

SG=405571000 = 40.557 say 40.6

Q2.

Recall the following

Mass = Volume * density and 1000 litres = 1m3.

i) mass of red fluid = 0.249 * (0.7 * 1000) = 174.3 kg.ii) mass of blue fluid = 0.133 * 2492 = 331.4 kg.

iii)

dPdZ

=pressuregradient=−ρg. For the red fluid = -(0.7*1000)*9.81 = -6867 Pa/m.

iv)

dPdZ

=pressuregradient=−ρg. For the blue fluid = -2492*9.81 = -24447 Pa/m.

v) Pressure difference between two points.

_______________________________________________________________________________________________WATS 1. Mark Russell (2005)Student number51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire

In this case the blue fluid is denser than the red fluid and so the blue fluid sits at the bottom of the tank.

Since there are 249 litres of red fluid i.e. 0.249 m3 and the tanks base dimensions are 1.8 * 1.54 the depth of the red fluid is simply 0.0898 m. Also since there are 133 litres of blue fluid i.e. 0.133 m3 the depth of the blue fluid is 0.0

_______________________________________________________________________________________________WATS 1. Mark Russell (2005)Student number51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire

CreditsThis resource was created by the University of Hertfordshire and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.

© University of Hertfordshire 2009

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_______________________________________________________________________________________________WATS 1. Mark Russell (2005)Student number 51 School of Aerospace, Automotive and Design Engineering

University of Hertfordshire