Week 1
Unit Conversions
Mass and Volume Flow
Ideal Gas
Newtonian Fluids, Reynolds No.
Week 2
Pressure Loss in Pipe Flow
Pressure Loss Examples
Flow Measurement and Valves
Pump Calcs and Sizing
4 m3 of wort is transferred from a kettle
through a 100 m long, 4 cm diameter pipe
with a roughness of 0.01 mm. The wort
flows at an average velocity of 1.2 m/s and
assume that its physical properties are the
same as those of water (μ = 0.001 Pa.s).
a) Determine the time required to transfer all
of the wort to the boil kettle, in min.
b) Determine the Reynolds Number.
c) Determine the pressure drop in the pipe.
Friction Losses in Pipes
L
2
P  2 C f v
D
Cf

found on Moody Chart handout
Determine the pressure drop of water, moving
through a 5 cm diameter, 100 m long pipe at an
average velocity of 5 m/s. The density of the
water is 1000 kg/m3 and the viscosity is 0.001
Pa.s. The pipe roughness is 0.05 mm.
Valves – Globe Valve
Single Seat
- Good general purpose
- Good seal at shutoff
Double Seat
- Higher flow rates
- Poor shutoff (2 ports)
Three-way
- Mixing or diverting
- As disc adjusted, flow to one channel
increased, flow to other decreased
Valves – Butterfly Valve
Low Cost
“Food Grade”
Poor flow control
Can be automated
Valves – Mix-proof Double Seat
Two separate sealing elements
keeping the two fluids
separated.
Keeps fluids from mixing
Immediate indication of failure
Automated, Sanitary apps
Easier and Cheaper than
using many separate valves
Valves – Gate Valve
Little flow control, simple, reliable
Valves – Ball Valve
Very little pressure loss, little flow control
Valves – Brewery Applications
Product Routing – Tight shutoff, material
compatibility, CIP critical
Butterfly and mixproof
Service Routing – Tight shutoff and high
temperature and pressure
Ball, Gate, Globe
Flow Control – Precise control of passage area
Globe (and needle), Butterfly
Pressure Relief – Control a downstream
pressure
Flow Measurement Principle:
Bernoulli Equation
1 2
P  v  gz  Constant
2
Notice how this works for static fluids.
Flow Measurement – Orifice Meter
P1
P2
2P
V  Cd A2

A


2
1 

A
1

Cd accounts for frictional loss,  0.65
Simple design, fabrication
High turbulence, significant uncertainty
2
Flow Meas. – Venturi Meter
P1
P2
2P
V  Cd A2

2
A

1   2 
A1 

Less frictional losses, Cd  0.95
Low pressure drop, but expensive
Higher accuracy than orifice plate
Flow Meas. – Variable Area/Rotameter
Forces  Drag  Weight
0C
1
drag 2
Av  mg
2
V  vA
Inexpensive,
good
flow
rate
indicator

Good for liquids or gases
No remote sensing, limited accuracy
Flow Measurement - Pitot Tube
P1
P2
v
1
2
P1  P2 
v
2
2
Direct velocity measurement (not flow rate)
Measure P with gauge, transducer, or
manometer
Flow Measurement – Weir
Open channel flow, height determines flow
Inexpensive, good flow rate indicator
Good for estimating flow to sewer
Can measure height using ultrasonic meter
Flow Measurement – Thermal Mass
Measure gas or liquid temperature
upstream and downstream of heater
Must know specific heat of fluid
Know power going to heater
Calculate flow rate
Flow Measurement – Magnetic
Faradays Law
Magnetic field applied to the tube
Voltage created proportional to velocity
Requires a conducting fluid (non-DI water)
Flow Measurement – Magnetic
Pumps
Suction
Pump
Delivery
Ps
Suction Head  h s  z s 
 h fs
ρg
Pd
Delivery Head  h d  z d 
 h fd
ρg
 Pd  Ps
Total Head  h d  h s  z d  z s   
 ρg
z = static head
hf = head loss due to friction

  h fd  h fs 

Pumps
Work  Force  Distance
Force
Work 
 Area  Distance
Area
Work Force
Distance
Power 

 Area 
time
Area
time
Power  ΔP  Volume Flowrate
PowerOutput  VP  V hg
Power Output
Power Input 
Pump Efficiency
Pumps
Calculate the theoretical pump power
required to raise 1000 m3 per day of water
from 1 bar to 16 bar pressure.
If the pump efficiency is 55%, calculate the
shaft power required.
Denisity of Water = 1000 kg/m3
1 bar = 100 kPa
Pumps
A pump, located at the outlet of tank A,
must transfer 10 m3 of fluid into tank B
in 20 minutes. The water level in
tank A is 3 m above the pump, the pipe
roughness is 0.05 mm, and the pump
efficiency is 55%. The fluid density is
975 kg/m3 and the viscosity is 0.00045
Pa.s. Both tanks are at atmospheric
pressure. Determine the total head and
pump input and output power.
Tank A
4m
Tank B
15 m
Pipe
Diameter, 50
mm
Fittings =
5m
8m
Pumps
Available NPSH  z s

Ps  Pvp 

h
ρg
fs
Need Available NPSH > Pump Required NPSH
Avoid Cavitation
z = static head
hf = head loss due to friction
Pumps
A pump, located at the outlet of tank A,
must transfer 10 m3 of fluid into tank B
in 20 minutes. The water level in
tank A is 3 m above the pump, the pipe
roughness is 0.05 mm, and the pump
efficiency is 55%. The fluid density is
975 kg/m3 and the viscosity is 0.00045
Pa.s. The vapor pressure is 50 kPa and
the tank is at atmospheric pressure.
Determine the available NPSH.
Tank A
4m
Tank B
15 m
Pipe
Diameter, 50
mm
Fittings =
5m
8m
Pump Sizing
1. Volume Flow Rate (m3/hr or gpm)
2. Total Head, h (m or ft)
2a. P (bar, kPa, psi)
3. Power Output (kW or hp)
4. NPSH Required
P  gh
Pumps
Centrifugal
Impeller spinning inside fluid
Kinetic energy to pressure
Flow controlled by Pdelivery
Positive Displacement
Flow independent of Pdelivery
Many configurations
Centrifugal Pumps
Delivery
Impeller
Volute
Casting
Suction
1 2
P  ρv  ρgz  Constant
2
Centrifugal Pumps
Flow accelerated (forced by impeller)
Then, flow decelerated (pressure increases)
Low pressure at center “draws” in fluid
Pump should be full of liquid at all times
Flow controlled by delivery side valve
May operate against closed valve
Seal between rotating shaft and casing
Centrifugal Pumps
Advantages
Simple construction, many materials
No valves, can be cleaned in place
Relatively inexpensive, low maintenance
Steady delivery, versatile
Operates at high speed (electric motor)
Wide operating range (flow and head)
Disadvantages
Multiple stages needed for high pressures
Poor efficiency for high viscosity fluids
Must prime pump
Centrifugal Pumps
H-V Chart
Increasing Impeller
Diameter
Head
(or P)
A
Volume Flow Rate
B
C
Centrifugal Pumps
H-Q Chart
Increasing
Efficiency
Head
(or P)
Required
NPSH
A
Volume Flow Rate
B
C
Centrifugal Pumps
H-Q Chart
Head
(or P)
A
Volume Flow Rate
B
C
Centrifugal Pumps
H-Q Chart
Head
(or P)
Required
Flow
Capacity
Actual
Flow
Capacity
Required
Power
Volume Flow Rate
Pressure Drop Example
Water flows through a 10 cm diameter, 300 m
long pipe at a velocity of 2 m/s. The density
is 1000 kg/m3, the viscosity is 0.001 Pa.s and
the pipe roughness is 0.01 mm. Determine:
a. Volume flow rate, in m3/s
b. Mass flow rate in kg/s
c. Pressure loss through the pipe, in Pa
d. Head loss through the pipe meters