ENG1005 Hydrostatics Formula Sheet Dr Ben Wetenhall School of Engineering Viscosity, μ y u • Viscosity/shear stress οΆu ο΄ =ο οΆy where π is dynamic viscosity, π is shear stress and ππ’ ππ¦ is velocity gradient • Kinematic viscosity π, π = Solid Boundary π π Pressure • In a confined system the pressure in liquids is always the same across a horizontal. πΉ π π= = π΄ π π = ππβ above atmospheric pressure π πΉ h area π area π΄ r Hydraulic Thrust and Centre of Pressure • The Hydraulic Thrust F acts through the Centre of Pressure (COP) πΉ = πππ΄βΰ΄€ Fluid where A is the area of the object and βΰ΄€ is the depth to the centre of gravity G Plane surface Centre of pressure: Pressure distribution G COP School of Engineering Find COP from either: 1. The centre of gravity of the pressure diagram or… 4 Centre of Pressure 2. From the formulas for the location of the COP along the slope (π₯0 ) and the depth to the COP (β0 ) πΉπ₯0 = ππ sin ππΌ0 β0 = β + 0 β0 π β πΌπ sin2 π π΄β A COP G π₯0 π₯ 0 where πΌ0 , πΌπ are the second moment of areas of the orange area about 0-0 and the centre of gravity (G) respectively and βΰ΄€ is the depth to G School of Engineering 5 Second moments of area of common shapes Parallel Axis Theorem ππ3 πΌπ = 12 d O O b πΌπ = h x b d School of Engineering x πΌπ₯π₯ π₯ πβ3 36 πβ3 = 12 ππ4 πΌπ = 64 G πΌπ = πΌπ + π₯ 2 π΄ 6 Horizontal Thrust on Curved Surfaces πΉπ₯ = ππβπ΄π πΉπ¦ = π€πππβπ‘ ππ πππ’ππ πππ ππππππ ππ¦ π‘βπ π π’πππππ = π£πππ’ππ ππ π¦πππππ€ π π’πππππ × π × π where π΄π is the vertically projected area of the curved surface and β is the depth to G of the vertically projected area π΅ π΄π β π πΉπ₯ Centre of pressure: • Fx acts through the centre of gravity of the pressure prism • Fy acts through the centre of gravity of the fluid displaced by the surface (G of the yellow surface) School of Engineering π΄
