1) While the flow of fluid follows the law τ =μ (du/dy)^{1.3}. It is observed that velocity distribution within fluid flow is given by:
U/U_{Max} = 2(y/h) - (y/h)^{3} / 3;
Where ‘h’ is a film thickness and UMax is a maximum velocity. Viscosity is 0.5 Ns/m^{2}. Compute shear stress at the solid surface when UMax =0.3 m/s and h=1cm. Viscosity of Newtonian fluid to induce same shear stress for same velocity profile and similar maximum velocity.
2) Tank ABCDE contains water up to a depth of 1 m and 2 m wide. Curve AB is defined by Z= X^{2 }and curve CD is a quadrant of circle of radius 0.3 m. Compute the resultant forces on AB and CD.
3) Deduce continuity equation in Cartesian co-ordinates.
4) Horizontal Venturimeter with inlet and throat diameters 300 mm and 100 mm respectively is used to measure flow of water. Pressure intensity at inlet is 130 KN/m^{2} whole the vacuum pressure head at throat= 350 mm of mercury. Suppose that 3 percent of head is lost in between inlet and throat. Determine the value of Cd (co-efficient of discharge) for Venturimeter, and rate of flow.
5) Resistance ‘R’ experienced by the partially submerged body depends upon velocity ‘V’, length of the body ‘L’, viscosity of fluid ‘μ’, density of fluid ‘ρ’, and gravitational acceleration ‘g’. Find a dimensionless expression for ‘R’.