2. An open vat of cross-sectional area 5.00 m has a circular hole in the bottom...

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2. An open vat of cross-sectional area 5.00 m² has a circular hole in the bottom for drainage. The area of the hole is 3.00×10 m² and the hole is exposed to the atmosphere. The hole is plugged and the vat is filled with water to a depth of 2.50 m. (Make a sketch.) a. Find the force of the water on the plug. (Hint: First find the gauge pressure of the water. Show work.) (P=1.00×10¹) (10 points) b. If the plug is removed, how fast does the water initially flow out of the hole? (Assume that the motion of the top of the water in the vat is negligible.) (Hint: p+pv² +pgy = constant or just use Torricelli's theorem.) (10 points) c. Use your result from part b to estimate the speed v with which the water level in the vat starts to fall at the instant the plug is removed. (Hint: Use the equation of continuity.) (10 points) 2. An open vat of cross-sectional area 5.00 m² has a circular hole in the bottom for drainage. The area of the hole is 3.00×10 m² and the hole is exposed to the atmosphere. The hole is plugged and the vat is filled with water to a depth of 2.50 m. (Make a sketch.) a. Find the force of the water on the plug. (Hint: First find the gauge pressure of the water. Show work.) (P=1.00×10¹) (10 points) b. If the plug is removed, how fast does the water initially flow out of the hole? (Assume that the motion of the top of the water in the vat is negligible.) (Hint: p+pv² +pgy = constant or just use Torricelli's theorem.) (10 points) c. Use your result from part b to estimate the speed v with which the water level in the vat starts to fall at the instant the plug is removed. (Hint: Use the equation of continuity.) (10 points)