Download Problem Sheet 1

Problem Sheet 1
1. Calculate the specific weight, density and specific gravity of one liter of a liquid which weights
7N.
2. If the velocity distribution over a plat is given by
2
u = y − y2 ,
3
in which u is the velocity in m/s at a distance y (in m) above the plate, determine the shear stress
at y = 0 and y = 0.15m. Take dynamic viscosity of the fluid= 8.63poises.
3. The space between two squire flat parallel plates is filled with oil. Each side of the plate is 60cm.
The thickness of the oil film is 12.5mm. The upper plate, which moves at 2.5m/s requires a force
of 98.1N to maintain the speed. Determine:
(i) The dynamic viscosity of the oil in poise.
(ii) the kinematic viscosity of the oil in stokes if the specific gravity of the oil is 0.95.
4. Determine the viscosity of a liquid having kinematic viscosity 6stokes and specific gravity 1.9.
5. Two large plane surfaces are 2.4cm apart. The space between the surfaces is filled with glycerine.
What force is required to drag a very thin plate of surface area 0.5m2 between the two large plate
surfaces at a speed of 0.6m/s, if:
(i) the thin plate is in the middle of the two plane surfaces.
(ii) the thin plate is at a distance of 0.8cm from one of the plane surfaces. Take the dynamic
viscosity of glycerine = 8.1 × 10−1 N s/m2 .
6. An open tank contains water upto a depth of 2m and above it an oil of specific gravity 0.9 for a
depth of 1m. Find the pressure intensity (i) at the interface of the two liquids, and (ii) at the the
bottom of the tank.
7. The right limb of a simple U-tube manometer containing mercury is open to the atmosphere while
the left limb is connected to a pipe in which a fluid of specific gravity 0.9 is flowing. The center of
the pipe is 12cm below the level of mercury in the right limb. Find the pressure of fluid in the pipe
if the difference in mercury level in the two limbs is 20cm.
8. The barometric pressure at sea level is 760mm of mercury while that on a mountain top is 735mm,
if the density of air is assumed constant at 1.2kg/m3 , what is the elevation of the mountain top.
9. Determine the total pressure on a circular plate of diameter 1.5m which is placed vertically in
water in such a way that the center of the plate is 3m below the free surface of water. Also find the
position of center of pressure.
10. A rectangular plane surface 2m wide and 3m deep lies in water in such a way that its plane makes
an angle of 30◦ with the free surface of water. Determine the total pressure and position of center
of pressure when the upper edge is 1.5m below the free water surface.