MET212 Homework #01 Please write solutions on separate papers. Answer all questions independently. (5 pts) The density of a sample of seawater is 1.99 slugs/ft3. What are the values in SI (kg/m3)? (10 pts) The kilogram-force is commonly used in Europe as a unit of force. (As in the U.S. customary system, where 1 lbf is the force exerted by a mass of 1 lbm in standard gravity, 1 kgf is the force exerted by a mass of 1 kg in standard gravity.) Moderate pressures, such as those for auto or truck tires, are conveniently expressed in units of kgf/cm2. Convert 32 psi to these units. (2 pts) Explain the physical meaning of psi and kgf/cm² (4 pts) Set up the unit conversion expression needed to convert from psi to kgf/cm². Clearly indicate which factors correspond to force conversion and which correspond to area conversion. (4 pts) Show the final conversion results (10 pts) Compute the pressure produced in the oil in a closed cylinder by a piston exerting a force of 12.0 kN on the enclosed oil. The piston has a diameter of 75 mm. (3 pts) Write down the equation used to compute the pressure produced in the oil by the piston. Express the piston area A in terms of the piston diameter. (4 pts) Set up the pressure calculation in SI base units, showing all unit conversions needed before evaluating the equation. (3 pts) Evaluate the expression and report the pressure in pascals (Pa). (10 pts) The specific gravity of benzene is 0.876. Calculate its specific weight and its density in U.S. Customary System units. (3 pts) Write down the equations that relate specific gravity, density, and specific weight. Clearly identify the reference fluid and the property values used in defining specific gravity (4 pts) Compute the density of benzene in U.S. Customary System units. Show any unit conversions used. (3 pts) Compute the specific weight of benzene in U.S. Customary System units. (10 pts) The kinematic viscosity and specific gravity of a liquid are and 0.79, respectively. What is the dynamic viscosity of the liquid in SI unit? (3 pts) Write down the relationship between kinematic viscosity, dynamic viscosity, and density. (3 pts) Using the given specific gravity, determine the density of the liquid in SI units. Show the intermediate step clearly. (4 pts) Compute the dynamic viscosity of the liquid and report the result in SI units. (15 pts) For a parallel plate arrangement shown in the figure below, it is found that when the distance between plates is 2 mm, a shear stress of 150 Pa develops at upper plate when it is pulled at a velocity of 1 m/s. Determine the viscosity of the fluid between the plates. Express your answer in SI unit. (4 pts) Explain what the Newtonian fluid assumption implies for the relationship between shear stress and velocity gradient in this flow. (4 pts) Write down the constitutive equation relating shear stress, viscosity, and velocity gradient. Clearly indicate how the velocity gradient is determined from the given geometry and motion. (3 pts) Set up the viscosity calculation using SI base units, showing any required unit conversions before evaluation. (4 pts) Evaluate the expression and report the dynamic viscosity of the fluid in SI units. (10 pts) Describe the difference between an SAE 20 oil and an SAE 20W oil.