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 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 bathyscape 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 enter it. The pressure inside the bathyscaphe is p =1.3 pare where perm=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 15 1.Cm7 You may assume that the pressure inside the bathyscaphe does not change while it is being filled with water H = 873.5m R=1.5m Figure 3: Schematic graph for Problem 3.

Answer 1

@ P = Pot Sgh Po = Atmospheric pressure P= .01 X100+ 1030 x 9.8 x 873.5 p = 8918109 Pa By bernoullins equation AP = I SV2 8918109 - 1-3 (1.01x165) = I x1030 v2 6 - 2 N = 130.62 dee 3 © volume of sphere Y TR3 V = 4T (1.5)2 = 9.424778 m3 VI VAT N = speed of water A = 1.07 xlo-4 m2 t = 20 min a = 1200 den 9.424778 = vx 1.07810-4 X 1200 = v= 73.402 m de

Date Page Now by Ap = IPv² 848 - 189 18109 - Pair) = 1x 1030 (73.402) 8918109 - Pair = 2774744.61 P Air = 6143364.4 Pa