Classical Mechanics Answers

1. A 10-cm ASME flow nozzle is installed in a 20-cm (horizontal) waterline. The attached manometer contains mercury (SG = 13.6) and water and registers a pressure difference of 42-cm. Calculate the discharge in the pipe.

2. Determine the discharge over an uncontracted horizontal weir when the upstream water depth is 7.0 ft. The sharp-crested weir is 9.0 ft long and 6.0 ft high.

1. The maximum flow rate in an 8-in. diameter (horizontal) waterline is 4.3 cfs. If a 4-in. Venturi meter is installed in the pipe to measure flow, estimate the necessary length of a vertical U-tube scale for the differential water-mercury (SG = 13.6) manometer.

2. A 50-cm diameter (horizontal) pipe contains a 20-cm Venturi meter. Determine the flow rate if the pressure difference reading between the throat and entry section in a water-mercury (SG = 13.6) manometer is 1.46 m.

6-36. Reconsider the helicopter in Prob. 6-35, except that it is hovering on top of a 2200-m-high mountain where the air density is 0.987 kg/m3. Noting that the unloaded helicopter blades must rotate at 550 rpm to hover at sea level, determine the blade rotational velocity to hover at the higher altitude. Also determine the percent increase in the required power input to hover at 2200 m altitude relative to that at sea level. Answers. 601 rpm, 9.3 percent

6-38 Water flowing in a horizontal 25-cm-diameter pipe at 8 m/s and 300 kPa gage enters a 90° bend reducing section, which connects to a 15-cm-diameter vertical pipe. The inlet of the bend is 50 cm above the exit. Neglecting any frictional and gravitational effects, determine the net resultant force exerted on the reducer by the water. Take the momentum-flux correction factor to be 1.04.

1. Water enters a 7-cm-diameter pipe steadily with a uniform velocity of 2 m/s and exits with the turbulent flow velocity distribution given by u = umax (I - r/R)1/7. If the pressure drop along the pipe is 10 kPa. determine the drag force exerted on the pipe by water flow.

2. A 5-cm-diameter horizontal jet of water with a velocity of 30 m/s relative to the ground strikes a flat plate that is moving in the same direction as the jet at a velocity of 20 m/s. The water splatters in all directions in the plane of the plate. How much force does the water steam exert on the plate?

1. A 2.5-cm-diameter horizontal water jet with a speed of Vj = 40 m/s relative to the ground is deflected by a 60° stationary cone whose bat diameter is 25 cm. Water velocity along the cone varies linearly from zero at the cone surface to the incoming jet speed of 40 m/s at the free surface.

2. A horizontal war jet impinges against a vertical flat plate at 30 ft/s and splashes off the sides in the vertical plane. If a horizontal force of 500 lbf is required to hold the plate against the water stream. determine the volume flow rate of the water.

1. The large water truck releaser water at the rate of 2400 liters/min through the 80-mm-diameter pipe. if the depth of the water in the truck is 1.5 m, determine the frictional force the road has to exert on the tires to prevent the truck from rolling.

2. The 80-kg man stands on the scale. If the bucket of water has a mass of 10 kg, and water is flowing into it at 0.001 m3/s from a 20-mm-diameter hose, determine the reading on the scale at this instant. Assume the bucket is large so that the rate at which the level of water in the bucket is rising can be neglected.

1. The lawn sprinkler consists of four arms that rotate in the horizontal plane. The diameter of each nozzle is 8 mm and the water is supplied through the hose at 0.006 m3/s and is ejected through the four nozzles into the atmosphere. Determine the torque required to keep the arms from rotating.

2. Water is discharged into the atmosphere from the pipe at 10 m/s. Determine the horizontal and vertical components of force and the moment that is developed at the fixed support A in order to hold the pipe in equilibrium. Neglect the resistance provided by the pipe at C, and the weight of the pipe and the water within it.

6-14 The hemispherical howl of mass m is held in equilibrium by the vertical jet of water discharged through a nozzle of diameter d. If the volumetric flow is Q, determine the height h at which the howl is suspended. The water density is pW.

6-43. A plow located on the front of a truck horizontally scoops up a liquid slush at the rate of 0.55 m3/s and throws it off vertically, perpendicular to its motion, i.e., theta = 90 degrees. If the truck is traveling at a constant speed of 5 m/s, determine the resistance to motion caused by the shoveling. The density of the slush is Ps = 1150 kg/m3.

1. An airplane is flying at an altitude of 10,500 m. Determine the gage pressure at the stagnation point on the nose of the plane if the speed of the plane is 450 km/h. How would you solve this problem if the speed were 1050 km/h? Explain.

2 The water pressure in the mains of a city at a particular location is 270 kPa gage. Determine if this main can serve water to neighborhoods that are 25 m above this location.

1. In a hydroelectric power plant, water enters the turbine nozzles at 800 kPa absolute with a low velocity. If the nozzle outlets am exposed to atmospheric pressure of 100 kPa. determine the maximum velocity to which water can be accelerated by the nozzles before striking the turbine blades.

2. A Pitot-static probe is used to measure the speed of an aircraft flying at 3000 m. If the differential pressure reading is 3 kPa, determine the speed of the aircraft

3. A piezometer and a Pitot tube are tapped into a 4-cm-diameter horizontal water pipe, and the height of the water columns are measured to be 26 cm in the piezometer and 35 cm in the Pitot tube (both measured from the top surface of the pipe). Determine the velocity at the center of the pipe.