**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 cm**

^{2}, 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 m**

^{2 }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 m^{3}.)**4. Water flows steadily along a horizontal tube of cross-sectional area 25 cm**

^{2}. The static pressure within the pipe is 1.3x10^{5}Pa and the total pressure 4x10^{5}Pa.**Calculate the velocity of the water flow and the mass of water flowing past a point in the tube per second.**