Student note : I need the table to be filled out and maybe like 4 calculation written out using the formulas I already did the lab i just need to show

work on how i got the answer 2 examples for each table need calculation shown for the first 4 line in the table/n , G.U.N.T. Gerätebau, Barsbüttel, Germany 12/2018 קון ני HM 150.05 6.9 HYDROSTATIC PRESSURE IN LIQUIDS Measured values worksheet Name: Date: Angle a: Lowest water level s STYREME Water level at upper edge of active area su Measurement Lever arm No.: Iw in mm 140 140 140 2 66 3 5 6 8 9 10 12 13 14 16 15 140. 140 280 080 280 280 Weight force Fw in N 1 2 3 4 4.5. 415 4 3 1.5. HAMBURG Measured values Water level hin mm 74 92 108 1२० 127 184 172 146 122 110. W 150.05 HYDROSTATIC PRESSURE IN LIQUIDS 9 rved, G.U.N. T. Goran Measured values worksheet 6 Appendix Name: Date: Angle a: Lowest water level sp Water level at upper edge of active area su Measurement Lever arm No. Iw in mm 33 KININ 1 185 CA 15 6 N 8 9 10 11 12 13 14 15 tidli 16 N.. 140 140 140 140 140 140 140 280 28.0 280 281 Weight force Fw in N Begge 1N 105 2.5 3 3,5 6 3.S 6.S 6 HAMBURG Measured values Water level hin mm st 48 58 67 74 82. 89 671 136 174 216 201 31 6.10 Analysis Measurement 11 12 13 No.: 5 69 7 t N Analysis worksheet Substitute force F, in N 2.0 3.1 Lever arm I, in mm 75.3 169.3 150.32 Name: Date: Moment M, in Nmm 150.6 526.5 240 Moment My in Nmm w 140 280 224 Variance in % 7.5 % 8.8%. 7.1%/n REFERENCES: G.U.N.T LABORATORY 1 Hydrostatic Pressure Lab 50 200- 150 100 Page 1 of 10 h F h level, F resultant force, A effective area, pressure profile, water level 50 150 — 100 OBJECTIVE: 1. To determine the hydrostatic force due to water acting on a partially or fully submerged surface; 2. To determine, both experimentally and theoretically, the center of pressure h Health and Safety 1. Wear masks, social distance and other protocols for doing the test is Mandatory for each session. 2. Safety glasses and CSA approved steel toe boots are MANDATORY. 3. Before any tests, inspect for the presence of any sharp edged. 4. Before any tests, detect for contaminants either naturally occurring or anthropogenic. 5. Please do not use hand or other stuff method for the detection of water. GEORGE BROWN Purpose The purpose of this experiment is to determine the relationship between the height of the water and the distribution of pressure. Additionally, the accuracy of this experiment will be determined by the balance of moments from the appended weight and resultant force. The understanding of hydrostatic pressure is important to civil engineers for the design of dykes, weirs, locks, and building plumbing. Theory Hydrostatic Pressure is the pressure exerted by gravity at a given point within a fluid that is at equilibrium. When a liquid is at rest and acts against a leveled surface, the hydrostatic pressure (Pn) can be determined by the following equation: Ph=pgt Where p is the density of water, g is the acceleration due to gravity, and t is any depth from the surface of the liquid. COLLEGE Yc A Page 2 of 10 01 a Ус Fp h Figure 1: Centre of Pressure Diagram Since hydrostatic pressure increases with depth and thus creates a triangular or trapezoidal distribution, the resultant force (Fp) is not applied at the centroid of the active surface (C in figure 1), but always slightly below it at a point known as the centre of pressure (D in figure 1). The distance from the centroid of the active surface to centre of pressure is represented by e. The angle at which the apparatus is tilted is represented by a, and yc represents the distance between the surface of liquid and the centroid of the active surface along the active surface. The resultant force is calculated by: Fp= Pc Aactive Pc = pgtc P2 Active surface Where to represents the depth from the surface of the water to the centroid of the active surface. The active area is the total surface area of the distributed hydrostatic pressure. For example, in this experiment the area would be the width of water vessel multiplied by the height of the pressure profile (h in Figure 1). If the water surface level goes above the height of the vessel, the area will then be a constant. The height and width of the water vessel is 100mm and 75 mm, respectively. †₁ N t₁ tc Active surface Aactiv t2 Figure 2: Resultant Force Diagram To find the centre of pressure you must first find the value of e, using a balance of moments established around a common point (01). Imagine an area (A) in front of the active surface, corresponding to the height of the pressure profile (h) and the two pressures P1 and P2. Then split the area (A) into two smaller areas A1 and A2, forming a triangle and a rectangle. Now the moment of the entire area is equal to the summation of the moments of the triangle and rectangle. Where A₁ = P₁. h, Solving for e results in: Fp ус Page 3 of 10 With the hydrostatic pressures P₁ = pgcosa (yc-1), TD. 811 A₁ A₂ •Ster P2 A₂ 01 Figure 3: Determining the Centre of Pressure 2/09 = 2hh Σ MO₁ h 2h A⋅ ( ²/2 + e) = A₁ · ²/2 + A ₂ · ² 3 P2-P1. 2 1 e = -h 6 e = = 0 . Planar center of gravity ·h, P₂ - P₁ P₂ + P₁ and 1 h² 12 yc A = A₁ + A₂ P₂ = pgcosa (y + 2) Centre of Pressure when Water Vessel is Tilted : The pressure profile is trapezoidal when the water level is above the active surface of the vessel and h remains constant at 100mm. This is represented in Figure 4, where s is the water surface level and st is the lowest point of the water vessel. The position of the centre of pressure (e), and the calculated lever arm distance (ID) is determined by the following equations, respectively: h = e = S-St COSX 1 (100 mm)² 12 (s - St) COS X Page 4 of 10 = Then the resultant force is determined by the formula Fp Pc=pg(s — St — 50mm * cos ∞) and Fp 50mm e = 50 Aact 250 th, 200 150 St Figure 4: Trapezoidal Profile (s> Sh) The pressure profile is triangular when the water level is below the height of the active surface for the vessel. This is represented in Figure 5, where s is the water surface level and St is the lowest point of the water vessel. The height of the pressure profile (h), position of the centre of pressure (e), and the calculated lever arm distance (ID) is determined by the following equations, respectively: 250 50mm-cosa 200 Sh 150 100 ID St PcAactive where: Aactive = 100mm 75mm S = 150 mm + e Sh lp = 200 mm Figure 5: Triangular Profile (s< Sh) 3 h Then the resultant force is determined by the formula Fp = PcAactive where: Centre of Pressure when Water Vessel is not Tilted : e = e = When the vessel is not angled the following equations that are used for a triangular and trapezoidal profile represented in the Figure 6 are as follows: P=pg ID 516 (s-St) 2 G Triangular profile Active surface Page 5 of 10 50 1 (100 mm)² 12 s-50 mm 250 la = 200 mm 200 150 and 100 S Aactive = h 75mm € Trapezoidal profile Active surface & 50 The equations to determine the position of the centre of pressure (e), the calculated lever arm distance (ID), the hydrostatic pressure (Pc), and active area (Aactive) are listed below respectively: And the resultant force is determined by the formula Fo = Figure 6: Pressure Distribution over a Leveled Water Vessel 250 Pc-pg-/2, Aactive = s. 75mm 200 PcA active. 150 100 50mm S la = 150 mm + e, Pc=pg(s - 50 mm), Aactive = 100 75mm s> Sh s< Sn And the resultant force is determined by the formula Fp= PcAactive. Within the apparatus, the appended weight creates a moment from the centre of motion. This is balanced by an equivalent resultant force applied by the water pressure. In Figure 7,