Question

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Problem 3 (4 pts.). A bathyscaphe (a small free-diving self-propelled deep-sea submersible), is a sphere of radius R- 1.5 m located 873.5 m below the sea level. (a) What is the pressure exerted on its surface (here you can neglect the size of the bathyscaphe compared to the depth of its immersion) and the buoyant force acting on it in the water (6) If a small leak is opened at the top of the bathyscaphe, with what speed will the water ente 10 The pressure inside the bathyscaphe is p = 1.3 Datum where Patm = 1.01 10° Pa is the atmospheric pressure. (C) We need to make sure that our bathyscaphe will not be completely filled with the water for at least 20 minutes. What air pressure should be created inside the bathyscaphe if the area of the opening is 1.07 cm"? You may assume that the pressure inside the bathyscaphe does not change while it is being filled with water. 2R to H = 873.5m R=1.5m Figure 3: Schematic graph for Problem 3.

Answer 1

Solution of above question is given below-

Pressure at dlepth h a ligui d P gh -Jo3 x 9.0x 873.5 Pressure exksol at surtace 8-56 x 166 Pa Pressure - Busyant tone 6n bathyscaphe VP 1.38 x 10 N (6) Water just bo lentk at reat .7 while just after leak iu siode Sphere has speed V. Ayptying Bernoul's Theorem betseen nd (2 Puiuts D - ht t4 iren 8-56X106 Cat surtaie) Pa - 1.3x)01X10 = 1.313X1 e P= 1.3 Ptm 1,313 X Jo +X0XV 16857X104 123.8t mis enteni n V.129. 84 m/s speed fwater

Vouume 4 sphere 19.137 s T0 Completely fil sphene Vo lune ta0 rate in 20 minutes 14.137 m 20 min 1200 See -2 1.178 X10 msee 1 Given Arer leak 1.67 cm Max Speeol t Vlmie flos Rate Anea fleale water V= 1.178X 102 1-87 X 10-9 ]) ן יס Bernoulli's Theorn P &.56x106 Pr 1) 2.498X 10 Pa 2.498 X106 Pa rented Prerdne