A sealed tank containing seawater to a height of 11.0 m also contains air above the water at a gauge pressure of 3.00 atm. Water flows out from the bottom through a small hole. How fast is this water moving? (Assume that the cross-sectional area of the tank (A1) is much larger than the cross-sectional area of the hole ( A2), so v_1 << v_2 and the (1/2)ρ(v_1)^2 term can be neglected.)

The lower section of a constricted pipe has a diameter of 8 cm. The upper section of the pipe, located 0.1 m above the lower section, has a diameter of 3 cm. The pressure at the lower section is 2.1 ×× 104 Pa, while the pressure in the upper section is 1 ×× 104 Pa. Assuming water moves through the pipe in a steady flow, calculate the speed (in m s-1) of the flow in the lower section. The density of water is 1000 kg m-3

Question 1 a) Consider the forces acting on an infinitesimal fluid element located at radius r inside a star, where the star is in hydrostatic equilibrium. Show that the buoyancy force acting on the fluid element may be written as Pe dv dt = -(Pe - p)g where Pe is the density inside the fluid element, p is the density of the gas in the surrounding gas at radius r, v is the velocity of the fluid element and g is local acceleration due to gravity. For full marks you should explain each step of your derivation. b) With the aid of a diagram, explain the condition required for convection to occur by considering the small displacement of a fluid element from its original equilibrium location within a star.

When a person inhales, air moves down the bronchus (windpipe) at 13.8 cm/s. The average flow speed of the air doubles through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction. Neglect the change of pressure due to change in height ?y in the wind pipe. If the pressure goes down then the pressure drop is negative. Use 1.20 kg/m33 for the density of air.

An automobile weighing 1.19 x 104 N has weight equally distributed over its wheels. The weight of the car causes each tire to be slightly flattened on the bottom so that there is a surface area in contact with the road. The gauge pressure of the air in the tire is 1.90 x 105 Pa (27.55 lb/in2). Find the area of contact, assuming that the only forces on the section of tire in contact with the road are the air pressure and the normal force exerted by the surface of the road. (The answer is not 0.06263 m2)

A level (horizontal) pipe contains a non-viscous, incompressible fluid with a density 1200 kg/m³ that is flowing steadily. At one position within the pipe, the pressure is 300 x 103 N/m2 and the speed of the flow is 20.0 m/s. At another position, the pressure is 200 x 103 N/m². What is the speed of the flow at this second position?