HYDRAULICS DEPARTMENT Name:_______________________________ Subject & Section:______________________ Date Performed:________________ Instructor:____________________________ Date Submitted:________________ EXPERIMENT NO. 3 HYDROSTATIC FORCE ON PLANE SURFACES Usually, engineers are confronted with problem of determining the force exerted by fluids acting on walls of container, such as pipes, tanks and concrete forms. Here, forces are due to the pressure, which is being exerted outward from the inside of the container. On other occasions, the problem maybe to determine the pressure exerted against submerged objects such as caissons, diving bells and balloons. Another common problem is the determination of forces acting on gates in the walls of these containers or submerged objects. Forces acting on containers or submerged objects are due to pressure of a gas, a liquid, or a solid. In the case of gas, pressure usually does not vary appreciably with elevation in vertical distances that are commonly considered. With liquids, however, the pressure will vary from atmospheric at free surface to tremendous magnitudes at great depths, such as the ocean. The actual absolute magnitude of the pressure depends on the atmospheric pressure, the depth of the point being considered, and the specific weight of the liquid involved. OBJECTIVE This experiment determines the hydrostatic force on a submerged and semi-submerged rectangular area. DERIVATION Let hs h d b = = = = vertical height from fulcrum to water surface vertical height from water surface to top of quadrant plane surface height of end surface of quadrant width of end face quadrant = 75 mm Consider a strip across the end face of the quadrant dx at a depth x, force on that strip = ρgxbdx. 12 (Please refer to your lecture notes) h x dF dx x d b = 75 mm From: P = γLh therefore P= γLx P= F/A = dF/dA therefore dF = PdA dF = γLxbdx dF hd h L gbxdx` Therefore, the total force on the end surface F gb h d h 2 2 -------------------------------------------- (1) 2 For partially submerged surface, h=0. Therefore, F gbd 2 2 13 Taking moments about the surface, Fx dFx Fx hd h Fx gbx 2 dx gb h d h 3 3 3 ----------------------------------------------- (2) Where x = depth of center of pressure Dividing Equation 2 by Equation 1: gb h d h 3 3 3 F gb h d h 3 3 3 2 gb h d h 2 2 3 2 2 3 3 2h 3dh 3d h d h x 3h 2 2dh d 2 h 2 x 2 3h 2 3hd d 2 x 32h d ---------------------------------------------- (3) For partially submerged surface, h=0 x 2d 3 Taking moment about the fulcrum APPARATUS Hydrostatic Pressure Apparatus Hydraulic Bench 14 LABORATORY PROCEDURE Place the apparatus on the hydraulic bench. Level the apparatus using the spirit level and adjustable feet. Ensure pump delivery valve is fully closed. Connect flexible supply hose to apparatus. Adjust the counterweight to balance the counter balance beam until the beam is level. Switch on the pump. Place a mass of approximately 50 grams on the pan. Open pump delivery valve and allow water into the tank until balance arm is horizontal, then close the pump delivery valve. Read height of water level on scale or torroid. Repeat the same procedure for various values of weight in the balance pan up to four trials. Stop Hydraulics Bench pump. Disconnect supply hose from the apparatus and allow apparatus to drain. Adjustable Screw Knife-edge Counter balance point hs 200mm h Weight Pan d Drain Plug FIGURE 1 15 APPLICATION OF PRINCIPLE 1. Comment on the variation of thrust with depth. 2. Comment on the relationship between the depth of the center of pressure and the depth of immersion. 3. For both 1 and 2, comment on what happens when the plane has become fully submerged. 4. Explain and comment on the discrepancies between the experimental and the theoretical results of the depth of center of pressure. 16 FINAL DATA SHEET NAME:_____________________________________________________ SUBJECT & SECTION:_______________________________________ SEAT NO. __________ DATE: _______________________ GROUP NO.___________________ EXPERIMENT NO.3 HYDROSTATIC FORCE ON PLANE SURFACE GROUP NO. 1 2 3 4 TRIAL NO. 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 W (g) h (mm) d (mm) h+d (mm) hs (mm) 17 x (mm) x + hs (mm) F (N) F(x+ hs) (N-mm) Wr (N-mm) GROUP NO. 5 6 TRIAL NO. 1 2 3 4 1 2 3 4 W (g) h (mm) d (mm) h+d (mm) hs (mm) 18 x (mm) x + hs (mm) F (N) F(x+ hs) (N-mm) Wr (N-mm)