2.138 When the Tucurui Dam was constructed in northern Brazil, the lake that was created covered a large forest of valuable hardwood trees. It was found that even after 15 years underwater the trees were perfectly preserved and underwater logging was started. During the logging process a tree is selected, trimmed, and anchored with ropes to prevent it from shooting to the surface like a missile when cut. Assume that a typical large tree can be approximated as a truncated cone with a base diameter of 8 ft, a top diameter of 2 ft, and a height of 100 ft. Determine the resultant vertical force that the ropes must resist when the completely submerged tree is cut. The specific gravity of the wood is approximately 0.6.

6) A sphere of radius R, made from a material of specific gravity SG, is submerged in a tank of water. The sphere is placed over a hole of radius a in the tank bottom open to the atmosphere, as shown in the diagram below. Assume a is much smaller than R. a) Develop a general equation for the range of specific gravities for which the sphere will float to the surface. b) For the values given, determine the minimum SG required for the sphere to remain in the position shown.

For the following population data for Carson City, Nevada (my home town), predict a reasonable range of population estimates for 2030 and 2050. Clearly explain your rationale.

2.145 When a hydrometer (see Fig. P2.145 and Video V2.8)having a stem diameter of 0.30 in. is placed in water, the stem protrudes 3.15 in. above the water surface. If the water is replaced with a liquid having a specific gravity of 1.10. how much of the stem would protrude above the liquid surface? The hydrometer weighs 0.042 lb. Hydrometer-Figure P2.145Fluidsurface

7) A rectangular container partially filled with water is accelerated in the x-direction.The initially flat water surface (dashed line) adjusts as shown (solid line). What is the magnitude of the acceleration?

A community of 510,000 people generates wastewater at a rate of 105 gallons/capita/day. The community is growing at a rate of 0.50 percent per year. When designing a new WWTF, design flows are typically projected 15 years into the future. Part a. Using the typical detention time, calculate the volume of primary clarification needed (in cubic feet). Part b. If ten parallel rectangular clarifiers are to be designed, provide the dimensions (in feet) of each tank. Use typical depths and length-to-width ratios.

The 18-ft-long lightweight gate of Fig. P2.117 is a quarter circle and is hinged at H. Determine the horizontal force, P,required to hold the gate in place. Neglect friction at the hinge and the weight of the gate.