Practice Problems on Bernoullis Equation C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Sep 15 bernoulli_01 A person holds their hand out of a car window while driving through still air at a speed of Vcar. What is the maximum pressure on the persons hand? Answer(s): 210maxcar2pppV Vcar Practice Problems on Bernoullis Equation C. Wassgren, Purdue University Page 2 of 17 Last Updated: 2010 Sep 15 bernoulli_02 Water is siphoned from a large tank through a constant diameter hose as shown in the figure. Determine the maximum height of the hill, Hhill, over which the water can be siphoned without cavitation occurring. Assume that the vapor pressure of the water is pv, the height of the water free surface in the tank is Htank, and the vertical distance from the end of the hose to the base of the tank is Hend. Answer(s): atm hillendvppHHg Hend Htank Hhill discharges into atmosphere constant diameter pipe Practice Problems on Bernoullis Equation C. Wassgren, Purdue University Page 3 of 17 Last Updated: 2010 Sep 15 bernoulli_03 Air flows through the Venturi tube that discharges to the atmosphere as shown in the figure. If the flow rate is large enough, the pressure in the constriction will be low enough to draw the water up into the tube. Determine the flow rate, Q, needed to just draw the water into the tube. What is the pressure at section 1? Assume the air flow is frictionless. Answer(s): 21 H 0 22 21112QgHAAatmACppp discharges into the atmosphere Q A1 A1 A2 section 1 section 2 air water tank is open to the atmosphere H Practice Problems on Bernoullis Equation C. Wassgren, Purdue University Page 4 of 17 Last Updated: 2010 Sep 15 bernoulli_05 You are to design Quonset huts for a military base. The design wind speed is U = 30 m/s and the free-stream pressure and density are p = 101 kPa and = 1.2 kg/m3, respectively. The Quonset hut may be considered to be a closed (no leaks) semi-cylinder with a radius of R = 5 m which is mounted on tie-down blocks as shown in the figure. The flow is such that the velocity distribution over the top of the hut is approximated by: 02sinrurRurRU The air under the hut is at rest. a. What is the pressure distribution over the top surface of the Quonset hut? b. What is the net lift force acting on the Quonset hut due to the air? Dont forget to include the effect of the air under the hut. c. What is the net drag force acting on the hut? (Hint: A calculation may not be necessary here but some justification is required.) Answer(s): 2surface ,top21 214sinpppCU 21 28 32LLCUR 0D hut R U r Practice Problems on Bernoullis Equation C. Wassgren, Purdue University Page 5 of 17 Last Updated: 2010 Sep 15 bernoulli_06 An air cushion vehicle is supported by forcing air into the chamber created by a skirt around the periphery of the vehicle as shown. The air escapes through the 3 in. clearance between the lower end of the skirt and the ground (or water). Assume the vehicle weighs 10,000 lbf and is essentially rectangular in shape, 30 by 50 ft. The volume of the chamber is large enough so that the kinetic energy of the air within the chamber is negligible. Determine the flowrate, Q, needed to support the vehicle. Answer(s): 2 skirtprojected2WAQA; Q = 2990 ft3/s fan Q skirt 3 in Practice Problems on Bernoullis Equation C. Wassgren, Purdue University Page 6 of 17 Last Updated: 2010 Sep 15 bernoulli_07 Oil flows through a contraction with circular cross-section as shown in the figure below. A manometer, using mercury as the gage fluid, is used to measure the pressure difference between sections 1 and 2 of the pipe. Assuming frictionless flow, determine: a. the pressure difference, p1-p2, between sections 1 and 2, and b. the mass flow rate through the pipe. Answer(s): 12H20Hgoilppg SG hSGHh442 1221 oiloiloil44 oil218D DppgmQHgDD section 1 (diameter, D1) section 2 (diameter, D2) oil (SG = 0.9) mercury (SG = 13.6) H h D1 = 300 mm D2 = 100 mm H = 600 mm h = 100 mm g Practice Problems on Bernoullis Equation C. Wassgren, Purdue University Page 7 of 17 Last Updated: 2010 Sep 15 bernoulli_08 A lightweight card of mass, m, can be supported by blowing air at volumetric flow rate, Q, through a hole in a spool as shown in the figure. The spool and card have diameter, D, and the spool has a large cavity with diameter, d. a. Determine the relationship between volumetric flow rate, Q, and the gap height, h. Clearly state all significant assumptions. b. Would the radial pressure gradient in the gap be greater for a viscous or an inviscid flow? Justify your answer. Answer(s): 2ln18D dhQmg D large cavity with diameter, d gap height, h card of mass, m volumetric flow rate, Q gravity Practice Problems on Bernoullis Equation C. Wassgren, Purdue University Page 8 of 17 Last Updated: 2010 Sep 15 bernoulli_