The velocity potential for a certain inviscid, incompressible flow field is given by the equation = 3ry- ( where o has the units of m/s when xand y are in meters. Determine the pressure at the point x= 1.6 m, y= 1.6mif the pressure at x 1my-1mis 2100 kPa. Elevation changes can be neglected, and the fluid is water. P2 kPa

The maximum depth recorded for a deep-sea dive is 308 m. Assuming that (i) the density of seawater is constant at 1.03 x 103 kg/m3 and (ii) the atmospheric pressure is 101 kPa, calculate the gauge pressure at this depth (in Pa and kPa).

(a) Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 32.6 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.(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 33.0 cm?

Calculate the absolute pressure at the bottom of a fresh-water lake at a depth of 31.6 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. (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 32.0 cm?

Suppose you measure a standing person’s blood pressure by placing the cuff on his leg 0.525 m below the heart. For this problem, assume that there is no loss of pressure due to resistance in the circulatory system (a reasonable assumption, since major arteries are large). The density of blood is 1.05×103 kg/m3 a. Calculate the systolic pressure you would observe, in units of mm Hgmm Hg, if the pressure at the heart was 120 over 80 mm Hg. Note that the top (and greater) number is the systolic pressure. b. Calculate the diastolic pressure you would observe, in units of mm Hgmm Hg, if the pressure at the heart was 120 over 80 mm Hg. Note that the bottom (smaller) number is the diastolic pressure.

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.

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