FD

ENSC3003 Fluid Mechanics - 2015 Assignment 6

Pumps & Pipework Systems / Flow in Porous Media

Questions 4 and 7 are to be submitted for Marking

Assignment Due : Before 4:00 pm on Monday, May 25th, 2015. The assignment must be submitted to LMS in a pdf file < 10 MB in size

1. A centrifugal pump is delivering water at a volumetric flow rate of 250 l/s. During a

test, gauges on the suction and discharge flanges of the pump measure (absolute) pressures of 80 kPa and 340 kPa respectively.

(a) Assuming that the pump suction is the same diameter as the pump discharge,

calculate the hydraulic power delivered by the pump. (b) If the pump efficiency is 76%, calculate the power that must be supplied to the

pump (the pump power) to achieve the stated duty. (c) If the pump suction diameter is 250 mm, and the pump discharge diameter is

200 mm, calculate the hydraulic power (assuming the same flow rate and pressure change)

2. A positive displacement pump is delivering a lime dosing solution at a volumetric

flow rate of 0.32 litres per minute. The change in pressure across the pump is 80 kPa. The efficiency of the pump is 80%. The specific gravity of the solution is 1.25.

(a) Assuming that the pump suction is the same diameter as the pump discharge,

calculate the pump power required at the stated duty point. (b) It becomes necessary to double the flow rate delivered by the pump. How would

you achieve this ? 3. A centrifugal pump transfers water from one reservoir to another via the pipework

illustrated in the figure attached overleaf. The pump curve is also attached.

(a) Calculate the system curve, and plot it on the pump curve provided. Determine the duty point for the system.

(b) A design review suggests reducing the flow rate by 8 %. Suggesting a method

by which this could be achieved.

QUESTION 3

P

33 feet

Fully OpenGate Valves

All bends;90 degree

Long radius

PipeworkLength 600 metresDiameter 200 mm

Roughness 0.15 mm

Swing CheckValve

0

20

40

60

80

100

120

140

0 0.05 0.1 0.15 0.2 0.25

HP

Flow rate (cubic metres/second)

Pump Curve - Question 3

4. A centrifugal pump is to be installed to transfer water (=1000 kg/m3, =0.001 Pas) from a reservoir to an elevated tank, as shown in the diagram below. To meet operational demands, the system must deliver a minimum volume flow rate of 220 litres/sec.

(a) The manufacturers pump curves for the proposed pump are attached

overleaf. Calculate the system curve (calculating a minimum of 3 points on the curve will be sufficient), plot it on the chart provided, and determine the duty point and impeller diameter needed to achieve the minimum specified duty. Charts for the fitting loss factors and pipe friction factor are attached. (NB please detach the finished chart and submit it with your assignment)

(b) For the duty point and impeller diameter determined in part (a), calculate

the power that must be supplied by the motor (in Watts). (c) If it is assumed that the friction losses in the inlet pipework and fittings may

be regarded as negligible for the purposes of determining NPSHA, is the proposed pump safe from cavitation at the proposed duty point? The vapour pressure of water at 293 K can be taken to be 0.238 m (H2O).

(d) Future plans for the system mean that in the long term the minimum

required flow can be reduced to 180 l/s. Determine the new duty point for the system, and describe the key modification to the system that you would recommend to achieve the reduced duty.

Pump Curve for Question 4

5. A centrifugal pump draws water at a flow rate of 0.14 m3/s from a tank via the pipework illustrated in the attached figure. At this flow rate, the pump requires a net positive suction head (NPSHR) of 7.2 metres (H2O). The vapor pressure of water at 20C is 17.535 mm Hg.

(a) Calculate the NPSHA at the pump. Is cavitation likely ? (b) If cavitation is likely, how would you propose reconfiguring the system to provide

sufficient NPSHA to avoid cavitation ?

P

4.0 metres Pipework(Total) Length 35 metresDiameter 200 mmRoughness 0.1 mm

Pipework(Total) Length 1 metre

Diameter 150 mmRoughness 0.1 mm

90 degree bendR/D = 0.7

Gate ValveFully Open Reducer

PumpCentreline

6. A reservoir holds water. The water flows by gravity through a sand filter housed in the exit pipe, as illustrated in the diagram below. At the end of the filter, the flow exits at atmospheric pressure. The sand grains are uniform, with an effective diameter of 1.25 mm. The void fraction in the filter is 0.32, and the filter extends over a length of 20 feet. Calculate the volume flow rate in the exit pipe (in m3/s).

7. A domestic water system incorporates an ion exchange resin water softener, as

illustrated in the diagram below. Inlet water enters via the top of the softener - the initial pressure head of 40 m (H2O) at the entrance to the softener. The water exits via the bottom of the softener, with a pressure head of 30 m (H2O) at the softener exit.

Within the softener, the water passes through a vertical (ie aligned with gravity) cylindrical column that is 4 inches in diameter and 3 feet long. The column is packed with spherical resin beads, each bead being 4 mm in diameter, to a total solid fraction of 0.64. The softener incorporates entry and exit volumes to ensure an even distribution of flow, as illustrated below.

For the inlet and outlet pressures prescribed above, determine the volume flow rate

of water (in m3/s) passing through the softener.

20 ft

Pipe D = 1 ft

H = 20 ft

8. Natural gas is being extracted from an underground rock/soil formation. Over time, the formation has eroded near the well, so that it has become less dense approaching the well, as illustrated in the diagram below. The permeability of the formation is accordingly a function of position within the bed, and, if the bed is modelled as one-dimensional, is given by

KD = Ko 1xK1

"

#$

%

&'

where K0 and K1 are constants, and L is the length of the formation. The pressures at the entrance and exit to the formation, P0 and PL, may be regarded as constant. Use the differential form of Darcy's Law to derive an equation giving the volume flow rate of crude oil through the formation as a function of; the length L of the formation the cross-sectional area of the formation (A) the inlet and outlet pressures P0 and PL the constants K0 and K1 the viscosity of the crude oil It may be assumed that the overall cross-sectional area of the formation is constant along the length of the formation, and that the flow is one dimensional and aligned with the X direction.

9. For spherical sand particles, with Dp = 0.015 in and SG = 2.2, and assuming

e=0.35: (a) Estimate the minimum fluidizing velocity if the fluid is air (Assume that the

density of air is 1.2 kg/m3, and the viscosity is 1.8 x 10-5 Pa s at standard atmospheric conditions).

(b) Estimate the minimum fluidizing velocity if the fluid is water (Assume that the density of water is 1000 kg/m3, and the viscosity is 0.001 Pa s)