FOURTH SEMESTER B.TECH. (ENGINEERING) DEGREE EXAMINATIONJUNE 2009

CE 04 404-FLUID MECHANICS

Part A

1. (a) Calculate the capillary rise in a glass tube of 2.5 mm diameter when immersed vertically inwater and mercury. Take surface tension cr = 0.0725 N/m for mercury in contact with air. Thespecific gravity for mercury is given as 13.6 and angle of contact = 130°.

(b) Briefly explain the various types of fluid flow.

(c) An open circular cylinder of 15 cm diameter and 100 cm long contains water up to a height of80 cm. Find the maximum speed at which the cylinder is to be rotated about its vertical axis sothat no water spills.

(d) Write the various classifications of orifices.

(e) Write the applications of siphon.

(f) Three pipes of length 800 m, 500 m, and 400 m and of diameters 500 mm, 400 mm and 300mm, respectively are connected in series. These pipes are to be replaced by a single pipe oflength 1700 m. Find the diameter of the single pipe.

(g) Write the various considerations in selecting the repeating variables (in Buckingham 7t theoremmethod).

(h) Briefly explain the various types of forces acting in moving fluid.

Part B

2. (a) Two large plane surface are 2.4 cm apart. The space between the surface is filled with glycerine.What force is required to drag a very thin plate of surface area 0.5 m2 between the two largeplane surface at a speed of 0.6 mls, if (i) the thin plate is in the middle of the two plane surfaceand (ii) the thin plate is at a distance of 0.8 cm from one of the plane surfaces? Take thedynamic viscosity of glycerine = 0.810 Ns/m2.

Or

(b) The velocity potential function is given by :

<D = - (xl) / 3_x2 + (x3y)/3+ i.(i) Find the velocity component in x and y direction.

(ii) Show that <I> represents a possible case of flow.

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FOURTH SEMESTER B.TECH. (ENGINEERING) DEGREE EXAMINATIONJUNE 2009

CE 04 404-FLUID MECHANICS

Part A

1. (a) Calculate the capillary rise in a glass tube of 2.5 mm diameter when immersed vertically inwater and mercury. Take surface tension cr = 0.0725 N/m for mercury in contact with air. Thespecific gravity for mercury is given as 13.6 and angle of contact = 1300

•

(b) Briefly explain the various types of fluid flow.

(c) An open circular cylinder of 15 cm diameter and 100 cm long contains water up to a height of80 cm. Find the maximum speed at which the cylinder is to be rotated about its vertical axis sothat no water spills.

(d) Write the various classifications of orifices.

(e) Write the applications of siphon.

(f) Three pipes of length 800 m, 500 m, and 400 m and of diameters 500 mm, 400 mm and 300mm, respectively are connected in series. These pipes are to be replaced by a single pipe oflength 1700 m. Find the diameter of the single pipe.

(g) Write the various considerations in selecting the repeating variables (in Buckingham 7t theoremmethod).

(h) Briefly explain the various types of forces acting in moving fluid.

2. (a) Two large plane surface are 2.4 cm apart. The space between the surface is filled with glycerine.What force is required to drag a very thin plate of surface area 0.5 m2 between the two largeplane surface at a speed of 0.6 mis, if (i) the thin plate is in the middle of the two plane surfaceand (ii) the thin plate is at a distance of 0.8 cm from one of the plane surfaces? Take thedynamic viscosity of glycerine = 0.810 Ns/m2.

Or

(b) The velocity potential function is given by :

cD = - (xy3) / 3_x2 + (x3y)/3+ y2.

(i) Find the velocity component in x and y direction.

(ii) Show that ~ represents a possible case of flow.

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3. (a) The water is flowing through a taper pipe of length 100 m having diameter 600 mm at theupper end and 300 mm at the lower end at the rate of 50lit/sate pipe has a slope of 1 in 30.Find the pressure at the lower end if the pressure at the higher level is 19.62 N/cm2.

Or

(b) A pipeline carrying oil of specific gravity 0.87, changes in diameter from 200 mm diameter ata position A to 500 m diameter at a position B which is 4 m at a higher level. If the pressure atA and Bare 9.81 N/cm2 and 5.886 N/cm2 respectively a!!d the discharge is 200 litis, determinethe loss of head and the direction of flow.

4. (a) The difference in water surface levels in two tanks, which are connected by three pipes inseries of length 300 m, 170 m and 210 m and of diameter 300 mm, 200 mm, and 400 mmrespectively is 12 m. Determine the rate of flow of water if co-efficient of friction are 0.005,0.0052 and 0.0048 respectively, considering minor losses and neglecting minor losses.

(b) Oil of relative density 0.9 and dynamic viscosity 2.5 poise is pumped through a 100 mmdiameter pipe 500m long at a rate of 2 litis.

(i) Find the Reynold's no of the flow.

(ii) Calculate the pressure required at the pump if the outlet end, which is free, is at 20mabove the pump level.

(iii) What should be the power input if the overall efficiency of the pump set is 65% ?

5. (a) A spillway model is to be built to a geometrically similar scale of 1/50 across a flume of600 mmwidth. The prototype is 15 m high and maximum head on it is expected to be 1.5 m :

(i) What height of model and what head on the model should be used?

(ii) If the flow over the model at a particular head is 12lit/sec, what flow per meter lengthof the prototype is expected?

(iii) If the negative pressure in the model is 200 mm, what is the negative pressure inprototype? Is it practicable?

(b) Find the displacement thickness, the momentum thickness and energy thickness for the velocitydistribution in the boundary layer given by :

2u I U = 2 (yl 8) - (yl 8) .

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