Problem 1: Water flows through a 1 cm diameter pipe with a speed of 1 m/s. What should be the diameter of the nozzle if water is to emerge at 2.1 m/s.
Problem 2: Water is flowing smoothly through a closed pipe system. At one point the speed of water is 3.0 m/s. While at another point 3.0 m higher, the speed is 4.0 m/s. At the lower point, the pressure is 80 kpa. Find the pressure at the upper point.
Problem 3: An aero plane wing is designed so that when the speed of the air across the top of the wing is 450 ms-1, the speed of air below the wing is 410 ms-1. What is the pressure difference between the top and bottom of the wing?
Problem 4: Water flows through a pipe whose internal diameter is 2.0 cm at a speed of 1.0 ms-1. What should be the diameter of the nozzle if water is to emerge at a speed of 4.0 ms-1.
Problem 5: Eight equal drops of oil are falling through air with a steady velocity of 0.1 ms-1. If the drops recombine to form a single drop, what would be the new terminal velocity?
Problem 6: Calculate the speed of efflux of kerosene oil from a narrow hole of a tank in which pressure is 4 atm. Density of kerosene oil is 72 kg m-3. (one atmosphere = 1.03 * 105 pa).
Problem 7: A small sphere of volume V falling in a viscous medium, acquire a terminal velocity vT. What will be the terminal velocity of a sphere of the same material and volume 8 V falling through the same medium?
Problem 8: Determine the radius of a water drop falling through air with a terminal velocity of 0.012 m/s. (Viscosity of air = 0.019 * 10-3 N s m-2 Density of air = 1.2 kg/m3
Density of water = 1.0 * 103 kg/m3).
Numerical examples from the text
Example 6.1: The radius of a small fog droplet is found to be 5.1 × 10-6m. The coefficient of viscosity of air is 1.9 × 10-5 kgm-1s-1. Find out the settling speed of the droplet in air.
Example 6.2: Velocity of water in 6 inch diameter pipe is 5 ft s-1. Find the velocity in a 3 inch diameter pipe which connects with it. Both pipes flow full.
Problem 6.3: A water hose of internal diameter 20 mm at the outlet discharges 30 kg of water in 60 s. Calculate the water speed at the outlet. Flow is steady and density of water is 1000 kg m-3.