Question

A tank with a curved cylindrical bottom, shown below in Figure 2, is completely filled with water of mass density 1000 kg/m3. a. Determine the horizontal and vertical components of the hydrostatic force on the curved cylindrical area ABCD. (4 marks) b. Calculate the magnitude and direction of the resultant force on the curved surface ABCD. (4 marks) c. Name the point through which this resultant force acts and state whether it lies above or below the centroid of the surface in contact with the water. (2 marks) Note: Sketch the problem showing all forces and direction (where appropriate). Also show all your workings. 6m 2m Not to scale 3m 20 Figure 2: A tank with a curved cylindrical bottom, which is filled with water.

Please show full working so I can learn to do it myself. Thank you!

Answer 1

Solution Free body diagram of the liquid Resultant force will be given by FR = F ² + f 22 mass density of fluid=1000kg/m n-am 4-FHF w vertical component of the force is given by the enpression F = Weight the fluid a svg = 1000X ILX 3)"x2x9.81 V-wl of tuc curve position T & quadrantshape) F = Fv = 61. 638KN Horizantal component of the force is given by the 2 expression F2 = FH = 89Ah (from botton) h = 4R = 4x2 3 TT 31 0.848m = 6x2 F2 = F f = 1000x 9.814 (682) X 0.848 = 99.826 KN (Area of rectangul Larportian A = LXb force Magnitude of the = 12 m2 FR = J FH²+ Fu2 = 5 (61.638]²4 (99-8262 IFR = 117.322 KN

disedian of the force tanot FH tano = 61-638 98.826 T0 = 31.690 | at the centre of pressure Resultant force will be act which will be ginen by h* - Ig t Ah I= Id4 or II RY = Tt m4 A = I R² = I x(212 substitute this = Tm2 value in abone expression h* = M +0.848 x 0.846 The = 8:03m aliae ft yh the As we seen after calculation hk h that means contre of buyure bul centroidof surface = 3-0.848 - 2.152m which is greater than contre of pressure so centroid of the surface lies below centre of pressure.