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Juice joust

Question: How is concentrated orange juice made, how does it differ from
freshly squeezed orange juice and what are the health benefits and pitfalls of
drinking each type?

Answer: Orange juice is concentrated by evaporation. Most processing plants
do this under reduced pressure to lower the boiling point. This also helps limit
heat damage to the juice.

Orange juice is concentrated to make it easier to transport around the world
and make the reconstituted product cheaper. The evaporation process does result
in a slight loss of flavour and vitamin C. Freshly squeezed juice costs more
because it is more expensive to transport.

Nicholas Shilton and Padraig Nally

Department of Agricultural and Food Engineering

University College Dublin

Answer: Until the early 20th century, some products were concentrated by
boiling them down to syrups, but that resulted in a cooked flavour.

One modern method is to freeze the juice until enough ice can be centrifuged
off. This is cheap and easy, but some flavourings, such as organic acids, freeze
out with the water. Concentration by evaporation at reduced pressure or even
freeze-drying are now routine. These methods give excellent products in liquid
or powder form—there is only a small loss of volatile flavours and no loss
of nutrients.

The main threat to flavour and health value is contact with oxygen. Oxidation
drastically spoils flavours and degrades vitamins A, C and E, as well as various
other nutrients.

Jon Richfield

Somerset West, South Africa

Tight squeeze

Question: When you squeeze the end of a hosepipe to make the opening smaller,
the water comes shooting out much faster. Why doesn’t this happen with a tap?
Instead, it just slowly reduces to a dribble.

There is an important difference between a nozzle or constriction at the end
of a pipe that is designed to create a narrow stream of fast-flowing water, but
which has little impact on the total flow rate, and a device like a tap that is
designed to decrease the flow of water by providing resistance equivalent to
that in an electric circuit. This difference, and the way that resistance is
introduced through turbulence, are explained below—Ed

Answer: Steady fluid flow in a pipe occurs when the available pressure
difference between the ends equals the pressure loss over that length. In pipe
flow, there is a variation of flow velocity over the cross-section of the pipe,
from zero at the pipe wall to the maximum on the pipe axis. The shearing of the
fluid causes the wall to exert a frictional drag on fluid which opposes the
driving pressure. If a flexible, uniform tube is lightly pinched at a midpoint
along its length, the fluid accelerates into the contraction and decelerates out
of it, with little loss of pressure.

If the tube is pinched tightly, the flow leaving the contraction becomes
audibly turbulent. The resulting transformation of smooth flow energy to random
motion incurs a pressure loss, and the flow rate decreases.

At the open end of any pipe, the pressure must equal that of the surrounding
air (atmospheric pressure). Unlike the former case, if you pinch the pipe here,
the flow ejected through the contraction does not have to decelerate as it
leaves.

The pressure drop and rate of flow along the pipe are therefore largely
unaffected by moderately squeezing the end of the tube. The ejection speed
increases because the product of the flow speed and cross-sectional area of the
tube must be the same everywhere (conservation of mass). However, the valve in a
tap is designed to control the pressure drop across it by introducing a sharp
change of cross section, thereby generating turbulence and altering the flow
rate.

Frank Fahy

Emeritus Professor of Engineering Acoustics

University of Southampton

Answer: If you were to measure the velocity within the tap valve itself you
would find that the flow speed is greatly increased relative to its speed
upstream. This is a result of the fundamental principle of mass conservation for
fluid flows which states that volume flow rate—flow speed multiplied by
cross-sectional area—is constant for incompressible fluids.

In other words, if you make the cross-sectional area smaller, the flow speed
must increase. But the mass-conservation principle says nothing about the size
of the volume flow rate. This depends on the mains water pressure and the
resistance offered by the tap or hosepipe, in a way analogous to Ohm’s law for
flow of electrical current.

A nozzle is designed to increase flow speed with minimal increase in
resistance. In contrast, a tap is effectively a variable resistor that allows
precise control of volume flow rate.

Bill Crowther

School of Engineering

University of Manchester

This week’s questions

Russian roulette: I was recently introduced to a fun mathematical trick
called Russian multiplication.

First take two numbers that you want to multiply and place them at the top of
two adjacent columns. Divide the number in the left-hand column by two. Ignore
any remainder and write the new number beneath the first. Repeat this step until
you are left with 1.

Now double the number in the right-hand column and write the answer below it.
Keep doubling all the way down until there are an equal number of figures in
both of the columns.

Delete the numbers in the right-hand column that are next to even numbers in
the left-hand column.

Now add up the remaining numbers in the right-hand column and you will find
that the total equals the result of multiplying the two original numbers at the
head of the lists. Why?

David Krause

Bradford, West Yorkshire

Tell me straight: It occurred to me that without an implement such as a
ruler, I would not be able to draw a straight line. But in order to produce a
ruler, I would need a straight line to compare it with. How were the first
completely straight tools produced?

Matthew Austin

Bracknell, Berkshire