problem 1:
a) A flow field is represented by a velocity potential function as given below:
A= c(2x^{2}-3y^{2})
Verify whether it is a valid function or not? If valid, then find out the corresponding stream function.
b) Define:
i) Stream function and
ii) Velocity potential function.
Describe their physical and mathematical concepts. Also list out the properties.
problem 2:
a) Cite any six exs where surface tension e_ect play a prominent role.
b) Derive the dimensions of:
i) Dynamic viscosity and Kinematic viscosity. Also obtain their units in MKS, FPS and SI systems.
problem 3: Petrol of specific gravity 0.8 is owing through a pipe inclined at 300 to the horizontal in upward direction. A venturimeter is fitted in this 25 cm diameter pipe; the ratio of areas of main and throat is 4 and the throat is at a distance of 1.2 m from inlet along its length.
The U- tube differential manometer connected to the inlet and throat section registers a steady reading of 5 cm of mercury; the tubes above the mercury being full of water. Find the discharge and pressure difference in kPa between the throat and entrance section. The meter has a discharge coefficient of 0.95 and relative density of mercury is 13.6.
problem 4:
a) Distinguish between rotational and irrotational flows.
b) Show that the velocity components given by u = 2x/t v = -y/t and w = z/t represent a possible fluid flow. Mention whether the flow is rotational or not.
problem 5:
a) State Newton's law of viscosity and give any four exs of its applications.
b) An oil of viscosity 8 poise is used for lubrication between a shaft and sleeve. The diameter of shaft is 0.4 m and it rotates at 180 rpm. find out the horsepower lost in the oil for a sleeve length of 120 mm. The thickness of the oil film is 1.3 mm.
problem 6:
a) A rectangular plate 0.5m wide and 1.6m deep is submerged in water in an inclined position. The maximum and minimum depths of the plate are 1.8m and 0.75m from the free surface. find out the hydrostatic force on one face of the plate, and the depth of centre of pressure.
b) A triangular plate of base width 3m and height 4m is immersed in water with its plan making an angle of 500 with the free surface of water. Determine the hydrostatic pressure force and the position of centre of pressure when the apex of the triangle lies 5m below the free water surface.