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41 Chapter 15 Fluids Practice Problems Fluids = m/V, H20= 1..000 x103 kg/m3. Pressure = Force / Area: P W = mg = gV F , P Patm mgh , [P]=N/m2 = 1 Pa, 1 atm = 1.01x105 Pa A 1 1 Mass Flow Rate: Av, Continuity : A1v1 A2 v2 , Bernoulli: P1 v12 gy1 P2 v22 gy2 2 2 Archimedes: Buoyant force is equal to the weight of fluid displaced fluid: BF: FB gV , If object fluid FLOAT Archimedes and Buoyancy 1 An oddly shaped solid object is submerged in a cylindrical beaker of water and is found to displace 0.08m3 of water. a) What is the buoyant force acting on the metal object? b. The above object weighs 1500 N in air. Will the object float or sink? Why? 2. A cube of material of density 2x103 kg/m3 is suspended in water with its top 3 meters below the surface of water. The cube measures 0.1 on each side. a) What is the buoyant force on it? b) Now the cube is suspended by a string that is connected to a scale. What is the apparent weight of the cube? 3. Calculate the velocity to which water can be squirted with the hose with a constant flow rate of 0.500 liters per second if it : a) emerges from the hose (r = 0.900cm) without the thumb b) emerges with the thumb reducing the radius to r = 0.250 cm. c)What is the maximum height the water can reach if it is shot straight up with the thumb? 4. A swelling in a blood vessel doubles its cross sectional area. By how much will the blood flow change as it moves through the enlarged area? The speed of blood (density = 1060 kg/m3) through a normal part of the vessel is v = .5 m/s. 41 Chapter 15 Fluids Practice Problems 5. Water flows at a speed of 20m/s through a tube of cross-sectional area 0.25 m2, as shown at point A. The Pressure at A is 1.8x105 Pa. a) the tube now runs uphill so that the distance above ground increases by 3.0 m. What is the pressure of the water at point B if we ignore fluid friction? b) The tube expands to a cross-sectional area of 1.00 m2 at point C. The average height above ground does not change. What is the speed of the water at point C, Ignoring fluid friction and assuming that the water speed at point B is 4.0 m/s? 6. Efflux Speed: A large tank is filled with water up to a depth of 15 m above ground. A spout located 10.0 m above the bottom of the tank is then opened. With what speed will water emerge from the spout? The tank is so large that the liquid level at the top changes very slowly. 7. Calculate the approximate force on a square meter of sail, given the horizontal velocity of the wind is 6.00 m/s parallel to its front surface and 3.50 m/s along its back surface. 8. AVenturi Meter is a device for measuring the speed of a fluid in a pipe. Find the mass flow rate and the speeds v1 an v2 if P2-P1 = 120Pa, A2=0.05m2 and A1 = 0.04m2 and the density of the fluid is 1/38 kg/m3.