Question 40 - A stream with volumetric flow rate Q enters a cylindrical tank and a stream with volumetric flow rate q exits the tank. The fluid has a constant heat capacity and density. There is no temperature change or chemical reaction occurring in the tank. Develop a model for determining the height of the tank, h. Let V is the volume, A is the cross sectional area, r is the density, m is the mass, where V and A are for the tank, r and m are for the fluid. The rate of mass of fluid accumulation, dm / dt = (Q - q) r. Prove the model to be dh / dt = (Q - q) / A.
Answer / kang chuen tat (malaysia - pen
Answer 40 - Mass of fluid in tank, m = Vr = hAr. Then d (hAr) / dt = (Q - q) r. Ar (dh / dt) = (Q - q) r leads to the answer A (dh / dt) = Q - q. Finally dh / dt = (Q - q) / A. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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Question 79 - (a) The American Petroleum Institute gravity, or API gravity, is a measure of how heavy or light a petroleum liquid is compared to water. Let SG = specific gravity of petroleum liquid, and V = barrels of crude oil per metric ton. Given the formula for API gravity = 141.5 / SG - 131.5 and V = (API gravity + 131.5) / (141.5 x 0.159), find the relationship of SG as a function of V. (b) An oil barrel is about 159 litres. If a cylinder with diameter d = 50 cm and height h = 50 cm is used to contain the oil, find the volume V of the cylinder in the unit of oil barrel by using the formula V = 3.142 x d x h x d / 4. (c) First reference : 1 cubic metre = 6.2898 oil barrels. Second reference : 1 cubic metre = 6.37 oil barrels. What are the 2 factors that cause the difference in such reference data?
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