In Exercises 55–58, F is the velocity field of a fluid flowing through a region in space. Find the flow along the given curve in the direction of increasing t. 55. F = -4xyi + 8yj + 2k r(t) = ti + t²j + k, 0
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- The velocity field of a fluid v (in meters per second) has divergence div(v)(P) = 3 at the point P = (2, 2, 2). Estimate the flow rate out of the sphere of radius 0.5 meter centered at P.Water in an irrigation ditch of width w = 3.22 m and depth d =1.04 m flows with a speed of 0.207 m/s.The mass flux of the flowing water through an imaginary surface is the product of the water’s density (1000 kg/m3) and its volume flux through that surface. Find the mass flux through the following imaginary surfaces: (a) a surface of area wd, entirely in the water, perpendicular to the flow; (b) a surface with area 3wd/2, of which wd is in the water, perpendicular to the flow; (c) a surface of area wd/2, entirely in the water, perpendicular to the flow; (d) a surface of area wd, half in the water and half out, perpendicular to the flow; (e) a surface of area wd, entirely in the water, with its normal 34.0° from the direction of flow.A 40 cm of honey (denisty = 1.36 g/m3) in one arm of an open U-tube manometer is found to balance a certain column height of vegetable oil (density = 0.91 g/m3). What is the measure of the height of oil?
- A submarine dives at 9.1m/s, at an angle of 15° to the surface of the water (i.e. downwards). Taking sea water density to be constant at 1002kg m^-3, what is the rate of change of pressure with time (Pa s^-1)?A worker uses high-pressure water to clean the inside of a long drainpipe. If the water is discharged with an initial velocity v0 of 11.5 m/s, determine (a) the distance d to the farthest point B on the top of the pipe that the worker can wash from his position at A, (b) the corresponding angle a.In testing a new material for shielding spacecraft, 126 small ball bearings, each moving ata supersonic speed of 410.1 m/s, collide headon and elastically with the material during a0.803 min interval.If the bearings each have a mass of 7.6 gand the area of the tested material is 0.77 m2,what pressure is exerted on the material?Answer in units of Pa.
- The terminal velocity of a copper of ball 2 milimiter falling through a tank of oil is 6.5cm/s . Determine the viscocity of oil if it's density is 1.5×103and the density of copper is 8.9*103kg/m3What is standard atmospheric pressure (in cm) measured by a barometer filled with water? (Given: Mercury is 13.6 times more dense than water.)A torricellian barometer consisting of an inverted tube of mercury in a dish of mercury. When the atmospheric pressure is exactly 1.00 atm, determine the height (h1) of the mercury in the tube?
- What fraction (f) of an iceberg floating in seawater is visible above the surface, if the density of freshwater ice is 917 kg/m³, while the density of seawater is 1024 kg/m³?The aircraft fuselage can be approximated as a circular cylinder for non-viscous aerodynamicanalysis. Given that the surface velocity of inviscid flow around a circular cylinder is:V = 2U∞sinθWhere q = 0 is a point on the axis of symmetry, show that the maximum dynamic pressure on thecylinder amounts to: 2 ρU∞2If P∞ at some distance upstream of the cylinder is 100kPa, and U∞ is 50m/s, determine the minimumstatic pressure on the cylinder surface for an air flow with density 1.225kg/m3The continuity equation for the flow of a fluid can be obtained as a logical consequence of the fundamental physical principle called: Answers: a) conservation of momentum. b) conservation of charge. c) conservation of mass. d) energy conservation.