Section A
Q1.
(a)
The velocity vector in an incompressible flow is given by V = (6xt + yz^{2})i + (3t + xy^{2})j + (xy - 2xyz - 6tz)k
(i) Verify whether the continuity equation is satisfied.
(ii) Determine the acceleration in x direction at point A(1, 1, 1) and t = 1.0.
(b)
Three tube wells of 25 cm diameter each are located at the three vertices of an equilateral triangle of side 100 m. Each tube well penetrates fully in a confined aquifer of thickness 25 m. Assume the radius of influence for these wells and the coefficient of permeability of the aquifer as 300 m and 40 m/day respectively.
(i) Calculate the discharge when only one well is pumping with a drawdown of 3 m.
(ii) What will be the percent change in discharge of this well if all the three wells were to pump such that the drawdown is 3 m in all the wells?
(c) Draw the schematic diagram of a gravity dam and indicate the major forces acting on it. Draw the diagram of the uplift force when (i) drain is not provided and (ii) drain is provided.
(d)
A city has the following recorded population :
Year 1971 : 60000
Year 1991 : 120000
Year 2011 : 180000
Estimate (i) the saturation population and (ii) expected population in the year 2031 by logistic curve method.
(e) A water contains 110 mg/L carbonate ion and 80 mg/L bicarbonate ion at a pH of 10. Calculate the alkalinity exactly at 25^{circ}C. Approximate the alkalinity by ignoring hydroxide and hydrogen ion. What is the percentage error in approximation?
