# Discharge

## Rate of Change of Volume of Sand in Conical Shape

**Problem**

A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute.

A. 2π ft/min | C. 3π ft/min |

B. 4π ft/min | D. 5π ft/min |

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## Problem 18 - Bernoulli's Energy Theorem

**Problem 18**

Figure 4-09 shows a siphon discharging oil (sp gr 0.90). The siphon is composed of 3-in. pipe from A to B followed by 4-in. pipe from B to the open discharge at C. The head losses are from 1 to 2, 1.1 ft; from 2 to 3, 0.7 ft; from 3 to 4, 2.5 ft. Compute the discharge, and make table of heads at point 1, 2, 3, and 4.

## Problem 17 - Bernoulli's Energy Theorem

**Problem 17**

In Figure 4-08 is shown a siphon discharging water from reservoir A into the air at B. Distance 'a' is 1.8 m, 'b' is 6 m, and the diameter is 150 mm throughout. If there is a frictional loss of 1.5 m between A and the summit, and 1.5 m between the summit and B, what is the absolute pressure at the summit in kiloPascal? Also determine the rate of discharge in cubic meter per second and in gallons per minute.

## Problem 16 - Bernoulli's Energy Theorem

**Problem 16**

A pump (Figure 4-07) takes water from a 200-mm suction pipe and delivers it to a 150-mm discharge pipe in which the velocity is 3.6 m/s. The pressure is -35 kPa at A in the suction pipe. The 150-mm pipe discharges horizontally into air at C. To what height h above B can the water be raised if B is 1.8 m above A and 20 hp is delivered to the pump? Assume that the pump operates at 70 percent efficiency and that the frictional loss in the pipe between A and C is 3 m.

## Problem 15 - Bernoulli's Energy Theorem

**Problem 15**

A pump (Figure 4-07) takes water from a 200-mm suction pipe and delivers it to a 150-mm discharge pipe in which the velocity is 2.5 m/s. At A in the suction pipe, the pressure is -40 kPa. At B in the discharge pipe, which is 2.5 m above A, the pressure is 410 kPa. What horsepower would have to be applied by the pump if there were no frictional losses?

## Problem 14 - Bernoulli's Energy Theorem

**Problem 14**

Water discharges through an orifice in the side of a large tank shown in Figure 4-06. The orifice is circular in cross section and 50 mm in diameter. The jet is the same diameter as the orifice. The liquid is water, and the surface elevation is maintained at a height h of 3.8 m above the center of the jet. Compute the discharge: (a) neglecting loss of head; (b) considering the loss of head to be 10 percent of h.

## Problem 13 - Bernoulli's Energy Theorem

**Problem 13**

The 150-mm pipe line shown in Figure 4-05 conducts water from the reservoir and discharge at a lower elevation through a nozzle which has a discharge diameter of 50 mm. The water surface in the reservoir 1 is at elevation 30 m, the pipe intake 2 and 3 at elevation 25 m and the nozzle 4 and 5 at elevation 0. The head losses are: from 1 to 2, 0; from 2 to 3, 0.6 m; from 3 to 4, 9 m; from 4 to 5, 3 m. Compute the discharge and make a table showing elevation head, pressure head, and total head at each of the five points.