A hot-air balloon consists of a basket hanging beneath a large envelope filled with hot air. A typical hot-air balloon has a total mass of 544 kg, including passengers in its basket, and holds 2.80 x 103 m3 of hot air in its envelope. If the ambient air density is 1.24 kg/m³, determine the density (in kg/m³) of hot air inside the envelope when the balloon is neutrally buoyant. Neglect the volume of air displaced by the basket and passengers.

A person is diving in a lake in the depth of h = 10.5 m. The density of the water is ρ = 1.0 x103 kg/m3. The pressure of the atmosphere is P0 = 1.0 x 105 Pa. The surface area of the top of the person's head is A = 0.0335 m2.  a. Express the absolute pressure at the depth of h, P, in terms of P0, ρ, and h.  b. Calculate the numerical value of P in Pa.  c. Express the magnitude of the force exerted by water on the top of the person's head F at the depth h in terms of P and A.  d.  Calculate the numerical value of F in N.

(a) A submersible vehicle is in a lake at a depth of 32.4 m. What is the absolute pressure (in Pa) at this depth? The density of the water in the lake is 1.00 ✕ 103 kg/m3, and the air above is at a pressure of 101.3 kPa.   (b) The submersible vehicle has a circular window with a diameter of 40.0 cm. What force (in N) is exerted by the water on the window of the vehicle at the depth from part (a)? (Enter the magnitude.)

(a) A submersible vehicle is in a lake at a depth of 26.6 m. What is the absolute pressure (in Pa) at this depth? The density of the water in the lake is 1.00 ✕ 103 kg/m3, and the air above is at a pressure of 101.3 kPa. ____Pa   (b) The submersible vehicle has a circular window with a diameter of 40.0 cm. What force (in N) is exerted by the water on the window of the vehicle at the depth from part (a)? (Enter the magnitude.) ____ N

A typical hot air balloon can carry 3–5 passengers in a wicker basket and has a total mass of  m = 470 kg  including passengers, not including the mass of air inside the balloon. The density of hot air inside the stationary balloon is  ?hot = 0.960 kg/m3  and the density of the cooler outside air is  ?cool = 1.22 kg/m3. Determine the volume of hot air required for the balloon to be in equilibrium so that it neither sinks nor rises in the air.

A Venturi meter is a device for measuring the speed of a fluid within a pipe. The drawing shows a gas flowing at speed v₂ through a horizontal section of pipe whose cross- sectional area is A₂ = 0.0619 m². The gas has a density of p = 1.30 kg/m³. The Venturi meter has a cross-sectional area of A₁ = 0.0393 m² and has been substituted for a section of the larger pipe. The pressure difference between the two sections is P₂ - P₁ = 90.8 Pa. Find (a) the speed v₂ of the gas in the larger original pipe and (b) the volume flow rate Q of the gas. P₂ Hi (a) Number i (b) Number A1 Lo P₁ Venturi meter Units Units ()

A submersible vehicle is in a lake at a depth of 32.0 m. What is the absolute pressure (in Pa) at this depth? The density of the water in the lake is 1.00 ✕ 103 kg/m3, and the air above is at a pressure of 101.3 kPa.   Pa (b) The submersible vehicle has a circular window with a diameter of 32.0 cm. What force (in N) is exerted by the water on the window of the vehicle at the depth from part (a)? (Enter the magnitude.)

(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 24.4 m. Assume the density of the water is 1.00 ✕ 103 kg/m3 and the air above is at a pressure of 101.3 kPa. Pa(b) What force is exerted by the water on the window of an underwater vehicle at this depth if the window is circular and has a diameter of 42.0 cm? N