Fluid Mechanics - Dec 2011

Mechanical Engineering (Semester 3)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1 (a) Differentiate between:
Weight density and mass density
Compressibilty and bulk modulus (6 marks) 1 (b) The space between the two square flat parallel plates is filled with oil.Each side of the plate is 720mm.The thikness of the oil is 15mm.the upper palte moves at 3m/s requires a force 120N to maintain the speed.Determine
dyanamic viscosity of the oil
kinematic viscosity of oil,if the secific gravity of oil is 0.95(7 marks) 1 (c) Calculate the capillary effect in milimeters in a glass tube of 4mm diameter ,when immersed in
Water and
mercury
the values of surface tension of water mercury at 20°C in contact with air are 0.07235N/m and 0.51N/m respectively.the specific weight of water at 20°C is eqal to 9790N/m³(7 marks) 2 (a) A U tube manometer containing mercury was used to find the negative in the pipe containg water.the right limb was open to the atmosphere .Find the vaccum pressure in the pipe,if the differnce of mercury level in the two limbs was 100mm and height oof water in the left limb from teh center of teh pipe was to be 40 mm below .sketches teh manometer with details (10 marks) 2 (b) Derive an expression for the total pressure force and depth of center of pressure for an inclined surface submerges in water(6 marks) 2 (c) A trapezoidal channel 2m wide at the bottom and 1m deep has side slopes 1:q.Determine
Toatal pressure
Center of pressure on the vertical gate closing the channel when it is full of water(4 marks) 3 (a) Derive the comtinuity equation in the three dimension in the differntial from and write the same for a steady incompressible flow(8 marks) 3 (b) Define the metacenter of floting body.Describe the analytical method of dermimig the metacentric height(8 marks) 3 (c) A wooden cylinder of circular section and uniform density ,specify garvity 0.6 is reqiured 0.6 is require dto float in an oil of specify gravity 0.8 if the diameter of the cylinder is 'd'and its lenghth'l' show the l can not exceed 0.817d for cylinder to float with its longitudianal axis vertical(4 marks) 4 (a) Derive the Euler euation of motion for a stedy flow and deduce the bermoulli euation of motio.mention the assumption made(10 marks) 4 (b) The water is flowing through a tapering pipe having diameter 300mm and 150mm at section 1 and 2 respectively.the discharge through the pipe is 40loter/sec.the section 1 is 10mm above datum and section 2 is 6m above datum.Find the intensity of presure at the section 1 is 400kN/m²(10 marks) 4 (c) Discuss the Bemoullis equation for real fluid(2 marks) 5 (a) The efficiency ? of a fan depends on the density '?' dyanamic vicosity ? of the fluid angular velocity ?,diameter D of the rotor and the discharge Q .Using the Buckinghsm's ? therom express ? in terms of dimensioanl parameter(10 marks) 5 (b) With a skecth derive an expression for the discharge through an inclined venturimeter for an upward flow(10 marks) 6 (a) Derive the Darcy-Weisbach equation.Derive it to the Chezzy's euation (10 marks) 6 (b) Water is to be supplied to the inhabitaion of a college campus through a supply main.The following data is given:
Distane of the reseivoir from the campus =3000m
Number in inhabiation =40000
consumption of water per day of each inhabitaion=180 liters
coefficient of fricationfor the pipe,f=0.007
If half of teh daily supply is pumped in 8 hours,determine the size of the supply main(8 marks) 6 (c) Define hydracules gradians and total line(2 marks) 7 (a) What is the Hagen -poiseuille formula ?Derive the expresion for the same (8 marks) 7 (b) A crude oil of velocity0.97 poise and relative density 0.9 is flowing through a horizontal circular pipe of diameter 100mm and length of 10m.calculate the differnce of pressure at two ends of the pipe .100kg of the oil is collected in a tank in 30 seconds.Assume laminar flow(8 marks) 7 (c) Write any two characteristic of laminar flow(4 marks) 8 (a) Derive an expression for displacement thickness of a flow over a plate(10 marks) 8 (b) A flat plate 1.5m × 1.5m moves at 50km/hour in the stationay air density 1.15kg/m^{3If the coefficient of drag and lift are 0.75 respectivly,determine
the lift force ,br>the drag force
the resultant force}(10 marks)