Ceng 231 Tutor 1

18/7/2014 CENG 231 Tutor 1

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CENG 231 Process Fluid MechanicsTutorial Examples 1

1. A hydraulic ram 200 mm in diameter and 1.2 m long moves wholly within a concentric cylinder 200.2 mm in

diameter, and the annular clearance is filled with oil of relative density 0.85 and kinematic viscosity 400 mm2 / s.

What is the viscous force resisting the motion when the ram moves at 120 mm / s?

( Ans.: 307.6 N )

2. The space between two large flat and parallel walls 25 mm apart is filled with a liquid of absolute viscosity 0.7 Pas. Within this space a thin flat plate, 250 mm x 250 mm is towed at a velocity of 150 mm / s at a distance of 6 mmfrom one wall, the plate and its movement being parallel to the walls. Assuming linear variations of velocity betweenthe plate and the walls, determine the force exerted by the liquid on the plate.

( Ans.: 1.493 N )

3. Calculate the pressure in the ocean at a depth of 2000 m assuming that salt water is (a) incompressible with a

constant density of 1002 kg / m3, (b) compressible with a bulk modulus of 2.05 GN / m2 and a density at the surface

of 1002 kg / m3.

( Ans.: 19.66 MN / m2, 19.75 MN / m2 )

4. Show that the ratio of the pressures (p2 / p1) and densities (r2 / r1) for altitudes h2 and h1 in an isothermal

atmosphere is given by

What increase in altitude is necessary in the stratosphere to halve the pressure? Assume a constant temperature of

-56.5 oC and the gas constant R = 287 J / kg K.

( Ans.: 4390 m )

5. Two small vessels are connected to a U-tube manometer containing mercury (relative density 13.56) and the

connecting tubes are filled with alcohol (relative density 0.82). The vessel at the higher pressure is 2 m lower inelevation than the other. What is the pressure difference between the vessels when the steady difference in level of themercury menisci is 225 mm? What is the difference of piezometric head? If an inverted U-tube manometer containinga liquid of relative density 0.74 were used instead, what would be the manometer reading for the same pressuredifference?

(Ans. : 44.2 kPa,3.495m, 35.82 m)

6. A manometer consists of two tubes A and B, with vertical axes and uniform cross-sectional areas 500 mm2 and

800 mm2 respectively, connected by a U-tube C of cross-sectional area 70 mm2 throughout. Tube A contains aliquid of relative density 0.8; tube B contains one of relative density of 0.9. The surface of separation between thetwo liquids is in the vertical side of C connected to tube A. Determine the additional pressure which, when applied tothe tube B, will cause the surface of separation to rise 60 mm in the tube C.

18/7/2014 CENG 231 Tutor 1


( Ans.: 171.1 Pa )

7. An oil and mercury manometer consists of a U-tube 5 mm diameter with both limbs vertical. The right-hand limb isenlarged at its upper end to 25 mm diameter. The enlarged end contains oil with its free surface in the enlargedportion and the surface of separation between mercury and oil is below the enlarged end. The left-hand limb contains

mercury only, its upper end being open to the atmosphere. The right-hand side is connected to a vessel containing

gas under pressure and the surface of separation is observed to fall 2 cm. Calculate the pressure of the gas in N / m2

if the specific gravity of mercury and oil are 13.6 and 0.85 respectively. The surface of the oil remains in the enlarged

ends.

(Ans.: 5.17x 103N/m2)

8. A manometer consists of an inclined glass tube which is connected to a meter cylinder standing upright: liquid fillsthe apparatus to a fixed zero mark on the tube when both cylinder and tube are open to the atmosphere. The upper

end of the cylinder is then connected to a gas supply at a pressure p and the liquid rises in the tube. Find an

expression for the pressure p in cm of water when the liquid reads y cm in the tube, in terms of inclination q of thetube, the specific gravity of the liquid s, and the ratio r of the diameter of the cylinder to the diameter of the tube.Hence determine the value of r so that the error due to disregarding the change in level in the cylinder will not exceed

0.1 % when q = 30 .

(Ans. :44.7)

9. An inclined manometer is required to measure an air pressure difference of about 3 mm of water with an accuracyof 3 %. The inclined arm is 8 mm diameter and the enlarged end is 24 mm diameter. The density of the manometric

fluid is 740 kg / m3. Find the angle which the inclined arm must make with the horizontal to achieve the requiredaccuracy assuming that the scale can be read with a maximum error of 0.5 mm.

( Ans.: 735' )

10. A manometer consists of a U-tube of diameter d, the upper part of each limb enlarged to diameter D. The smalltube contains liquid of relative density sm and on top of this in each limb is a liquid of relative density s. The free

surfaces are in the enlarged parts and the surfaces of separation between the two liquids of density sm and s are in the

small tube and initially level. Show that the pressure difference in a gas which, when applied across the manometer,produces a difference in the interface levels of h in the small tube is given by

r - density of water

where the free surfaces remain in the enlarged ends. Also show that the sensitivity becomes greatest when the valueof s approaches sm.

In such a manometer the ratio D / d = 5, one of the manometer liquids is water and the other of relative density 0.95.Find the applied pressure difference required to produce a difference of interface levels h of 1 cm.

( Ans.: 8.63 Pa )

11. A spherical air bubble rises in water. At a depth of 9m its diameter is 4mm. What is its diameter just as it reachesthe free surface where the pressure is 101.3 kPa? You may assume that surface tension effects are negligible.

18/7/2014 CENG 231 Tutor 1


( Ans.: 4.93 mm )

18/7/2014 CENG 231 Tutor 1


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