Fluid Mechanics: Examples and Answers1. Pressure and Manometers

SG=13.6

2. Fluid Dynamics

3. Application of Bernoulli Equation

5. Flow in Pipes1.

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6. Pumping of Fluids1.

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7. Motion of particles in a fluid: Sedimentation1. What is the terminal velocity of a spherical steel particle, 0.40 mm in diameter, settling in an oil of density 820 kg/m3 and viscosity 10 mNs/m2? The density of steel is 7870 kg/m3.

2. A finely ground mixture of galena and limestone in the proportion of 1 to 4 by mass is subjected to elutriation by an upward-flowing stream of water flowing at a velocity of 5 mm/s. Assuming that the size distribution for each material is the same, and is as shown in the following table, estimate the percentage of galena in the material carried away and in the material left behind. The viscosity of water is 1 mNs/m2 and Stokes’ equation may be used.

The densities of galena and limestone are 7500 and 2700 kg/m3, respectively.

3. What is the mass of a sphere of material of density 7500 kg/m 3 whose terminal velocity in a large deep tank of water is 0.6 m/s?

4. What will be the terminal falling velocity of a glass sphere 1 mm in diameter in water if the density of glass is 2500 kg/m3?

5. What is the mass of a sphere of density 7500 kg/m3 which has a terminal falling velocity of 0.7 m/s in a large tank of water?

8. Filtration1. A slurry is filtered in a plate and frame press containing 12 frames, each 0.3 m square and 25 mm thick. During the first 180 s the pressure difference for filtration is slowly raised to the final value of 400 kN/m2 and, during this period, the rate of filtration is maintained constant. After the initial period, filtration is carried out at constant pressure and the cakes are completely formed in a further 900 s. What is the volume of filtrate collected per cycle?In an experiment, a sample of the slurry had previously been tested with a leaf filter of 0.05 m2 filtering surface using a vacuum giving a pressure difference of 71.3kN/m2. The volume of filtrate collected in the first 300 s, was 250 cm3 and, after a further 300 s, an additional 150 cm3 was collected. It may be assumed that the cake is incompressible and that the cloth resistance is the same in the leaf as in the filter press.

2. It is required to filter a slurry to produce 2.25 m3 of filtrate per working day of 8 hours.The process is carried out in a plate and frame filter press with 0.45 m square frames and a working pressure difference of 348.7 kN/m2. The pressure is built up slowly over a period of 300 s, during this period, the rate of filtration is maintained constant and 0.193 m3 of filtrate is collected. When a sample of the slurry is filtered, using a pressure difference of 66.3 kN/m2 on a single leaf filter of filtering area 0.05 m2, 400 cm3 of filtrate is collected in the first 300 s of filtration and a further 400 cm3 is collected during the following 600 s. What is the minimum number of frames that need be employed and the total time to collect the total volume of filtrate? The resistance of the filter cloth may be taken as the same in the laboratory tests as on the plant.

9. Fluidization1. Oil, of density 900 kg/m3 and viscosity 3 mNs/m2, is passed vertically upwards through a bed of catalyst consisting of approximately spherical particles of diameter 0.1 mm and density 2600 kg/m3. At approximately what mass rate of flow per unit area of bed will (a) fluidisation, and (b) transport of particles occur?2. Calculate the minimum velocity at which spherical particles of density 1600 kg/m3 and of diameter 1.5 mm will be fluidised by water in a tube of diameter 10 mm.