MEK 307 FLUID MECHANICS 2011-2012 Fall Term HOMEWORK 1 ...

MEK 307 FLUID MECHANICS2011-2012 Fall TermHOMEWORK 1Due Date: 27.10.20111. Estimate the minimum absolute pressure (in pascals) that can be developed at the inlet of a pump toavoid cavitation if the fluid is ethyl alcohol at 20 o C.2. a) A vacuum gage connected to a chamber reads 30 kPa at a location where the barometric reading is750 mmHg. Determine the absolute pressure in the tank. (ρ Hg =13 590 kg/m 3 )b) A pressure gage connected to a tank reads 500 kPa at a location where the atmospheric pressure is94 kPa. Determine the absolute pressure in the tank.c) The absolute pressure in water at a depth of 5 m is read to be 145 kPa. Determine the absolutepressure at a depth of 5 m in a liquid whose specific gravity is 0.85 at the same location.3. A 1.5 mm diameter tube is inserted into an unknown liquid whose density is 960 kg/m 3 , and it isobserved that the liquid rises 5 mm in the tube, making a contact angle of 20°. Determine the surfacetension of the liquid.4. Derive a relation for the capillary rise of a liquid between two large parallel plates at a distance tapart inserted into the liquid vertically. Take the contact angle to be φ.5. A thin 20 cm x 20 cm flat plate is pulled at 1 m/s horizontally through a 3.6 mm thick oil layersandwiched between two plates, one stationary and the other moving at a constant velocity of 0.3m/s, as shown in the figure. The dynamic viscosity of oil is 0.027 Pa.s. Assuming the velocity in eachoil layer to vary linearly, a) plot the velocity profile and find the location where the oil velocity iszero and b) determine the force that needs to be applied on the plate to maintain this motion.6. The viscosity of a fluid is to be mesaured by a viscometer constructed of two 75 cm long concentriccylinders. The outer diameter of the inner cylinder is 15 cm, and the gap between the two cylinders is0.12 cm. The inner cylinder is rotated at 200 rpm, the torque is measured to be 0.8 Nm. Determinethe viscosity of the fluid.

7. The gage pressure of the air in the tank shown in the figure is measured to be 45 kPa. Determine thedifferential height h of the mercury column.8. Two water tanks are connected to each other through a mercury manometer with inclined tubes. Ifthe pressure difference between the two tanks is 20 kPa, calculate a and θ. (SG=13.6)9. The air above the liquid is under a pressure of 30 kPa gage and the specific gravity of the liquid inthe tank is 0.80. If the rectangular gate is 1.0 m wide and if y 1= 1.0 m and y 2= 3 m, what force P isrequired to hold the gate in place?10. The rectangular gate is 10 m x 4 m in dimension and is pin connected at point B. The surface onwhich the gate rests at A is frictionless and the water surface is 6 m above point B. The gate is to beopened from its lower edge by applying a normal force at its center. Determine the minimum force Frequired to open the water gate.