Practice Problems

1. A liquid has a density of 900 kg/m³. What pressure does it exert at 5 m depth?
2. Water flows through a horizontal pipe of cross-section 0.04 m² at 3 m/s. If the pipe narrows to 0.01 m², calculate the speed in the narrow section.
3. A horizontal pipe has water moving at 2 m/s with pressure 1.2 × 10⁵ Pa. Velocity at another section is 5 m/s. Find the pressure there (ρ = 1000 kg/m³).
4. Explain qualitatively how increasing viscosity affects flow rate in a pipe.
5. A U-tube contains two different liquids of densities 800 kg/m³ and 1000 kg/m³. If the heights are 0.4 m and 0.32 m respectively, verify hydrostatic equilibrium.
6. Air moves over the top of a roof at 15 m/s while under the roof it is nearly stationary. Using Bernoulli’s principle, explain why this generates lift.
7. A vertical water column is 6 m high. Calculate the pressure at the base in kPa.
8. In a pipe of varying cross-section, the flow rate is 0.06 m³/s. If a section has an area of 0.02 m², what is the velocity there?
9. A pipe carrying oil has velocity 2 m/s at a wide section. In a narrow section, velocity is 6 m/s. Find pressure difference between sections (ρ = 850 kg/m³).
10. Discuss why Bernoulli’s principle cannot be applied to viscous, turbulent flows without corrections.