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## Determine the correct diameter for the piping and control valve so that the pressure drop in the piping system is 15 psig at a velocity of 8 fps if the fluid is benzene and the volumetric flow rate is 1000 gallons per minute

## LM 5 Homework Assignment

**Moving Fluids**

**1**. McCabe Problem 8.1a

**2**. McCabe Problem 8.2. *(Recognize that a “reboiler” is a heat exchanger in which a liquid is being vaporized into a gas. Therefore, the pressure in the reboiler is equal to the vapor pressure of the liquid at that temperature.)*

**3**. Use ChemCad to solve the following problem.

Consider a piping system connecting a vessel operating where the discharge pressure is 150 psig and another pressure vessel where the inlet operating pressure is 135 psig. The fluid in the piping system is at 140 oF. The piping system consists of schedule 40, carbon steel piping and fittings as shown in the following sketch:

Globe Valve

__Distances at control valve (CV):__

From 90o elbow to reducer = 1 ft;

Length of reducer is 3 inches

From reducer to CV = 0.5 ft

From CV to expander = 0.5 ft

Length of expander is 3 inches

From expander to 90o elbow is 1 ft

2nd

Pressure Vessel

1st

Pressure Vessel

a) Determine the correct diameter for the piping and control valve so that the pressure drop in the piping system is 15 psig at a velocity of 8 fps if the fluid is benzene and the volumetric flow rate is 1000 gallons per minute

*A common rule of thumb used to design piping systems is that the velocity of a flowing liquid should be in the range of 6-10 feet per second (fps). For our problem, let’s use 8 fps. Also, we usually make control valves one to two pipe sizes in diameter smaller than the connecting piping. For this problem, let’s assume that our control valve size is one standard pipe size inch smaller than the surrounding piping (that is, if the pipe is 4” schedule 40 diameter, the control valve is a 3” diameter valve, if 3” diameter pipe make the control valve 2”; if 2” diameter pipe make the control valve 1.5”, if the pipe is 6” make the control valve 4”, if the pipe is 8” make the control valve 6”). Other than the control valve and the connecting pipe spools (which should have the same diameter as the control valve), assume that all the rest of the piping and fittings are the same diameter.*

b) Repeat part a) if the fluid is methane gas and the flow rate is 570,000 standard cubic feet per hour.

*A common rule of thumb used to design piping systems is that the velocity of a flowing vapor should be in the range of 60-100 fps. For our problem, let’s use 80 fps.*

**4**. It is proposed to pump 10,000 kg/hr of toluene at 95 oC and 1 atm absolute pressure from the reboiler of a distillation tower, E1 to a second distillation tower, C2. Here is a description of the piping run between E1 and C2:

· Segment A (E1 to P1): 3 meters of straight pipe (all pipe is Schedule 40), 90o elbow turning flow upwards, 1 meter of straight pipe, 90o elbow turning flow horizontal, 100% open gate valve.

· Pump, P1: increases pressure from 1 atm at E1 to 1.8 atm at C2.

· Segment B (P1 to control valve): 8 meters of straight pipe, 90o elbow making horizontal turn, 2 meters of straight pipe, 90o elbow turning flow upwards, 2 meters of straight pipe, 100% open gate valve, 2 meters of straight pipe, 90o elbow turning flow horizontal, 15 meters of straight pipe, 90o elbow turning flow downwards, 4 meters of straight pipe, straight-through run on a tee (other tee branch has a 100% closed globe valve attached to it), 90o elbow turning flow horizontal, reducer to decrease pipe size by one nominal inch pipe size, 0.5 meter straight pipe.

· Control valve: globe valve.

· Segment C (control valve to C2): 0.5 meter straight pipe, expander to increase pipe size by one nominal inch pipe size, 90o elbow turning flow upwards, straight-through run on a tee (other tee branch has a 100% closed globe valve attached to it), 3.5 meters of straight pipe, 90o elbow turning flow horizontal, 3 meters of straight pipe.

a) Using ChemCad and a velocity of around 8 ft/sec in the piping (except around the control valve where the velocity is increased), determine the standard nominal pipe diameter for segments A-C (all the same).

b) Using ChemCad, determine the theoretical horsepower required by the pump.

c) If the combination of pump and motor are 65% efficient, what size (in terms of power) must the pump’s motor be?

**5.** You need to select a pump to move a liquid (=1500 kg/m3, =90 cp, pvap=0.05 atm) from a pressurized underground reservoir to a vented above ground tank at a rate of 10 gpm. Which of the four pumps described below do you recommend?

Pump | Max. Head (ft) |
Max. Capacity (gpm) |
Max. Efficiency (%) |
NPSH Required (ft) |

A | 35 | 16 | 45 | 15 |

B | 29 | 20 | 75 | 8 |

C | 24.5 | 8 | 60 | 10 |

D | 14 | 12 | 50 | 6 |

10 ft

100 ft

6″ PVC – 110 ft

1 – 900 elbow

1 – ball valve

6″ PVC – 20 ft

1 – ball valve

P = 5 atm

5

10

15

20

25

30

35

40

05101520

Capacity (gpm)

Pump Head (ft)

A

B

C

D