Fluids in motion
(Density of water = 1000 kgm-3)
1. A large tank containing water has a small hole near the bottom of the tank 1.5 m below the surface of the water.
(a) What is the velocity of the water flowing from the hole?
(b) Where must a second hole be drilled so that the velocity of water leaving that hole is half that of water flowing through the first hole?
2. Water flows along a horizontal pipe of cross-sectional area 30 cm2, The speed of the water is 4 m s-1, but this rises to 7.5 m in a constriction in the pipe.
What is the area of this narrow part of the tube?
3. What is the maximum weight of an aircraft with a wing area of 50 m2 flying horizontally, if the velocity of the air over the upper surface of the wings is 150 ms-1 and that over the lower surface 140 ms-1. (Take the density of air to be 1.29 kg m3.)
4. Water flows steadily along a horizontal tube of cross-sectional area 25 cm2. The static pressure within the pipe is 1.3x105 Pa and the total pressure 4x105 Pa.
Calculate the velocity of the water flow and the mass of water flowing past a point in the tube per second.