Water speed records
The water in my local river has risen approximately 25 per cent because of recent rainfall, yet the speed of flow is approximately four times the normal rate. Given that the flow is still down the same gradient, why the massive speed increase?
鈥� Anybody who has played pooh sticks by dropping twigs in a river will know the flow is faster in the middle of the stream and slower at the sides where friction between moving water and the banks reduces the velocity.
A very narrow, shallow stream has most of its water in close contact with the bed and banks 鈥� the 鈥渨etted perimeter鈥� 鈥� and so uses a high proportion of its energy in overcoming the frictional effect. On the other hand, a deeper, wider river with a greater cross-sectional area (calculated as width multiplied by mean depth) has a mass of water flowing in the middle of its channel unimpeded by frictional effects, allowing it to move at a higher mean velocity.
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A burbling mountain stream leaping and surging down a steep gradient between boulders may seem fast, but usually a slow-flowing, broad meandering river moving down a gentle gradient has the greater mean velocity. Likewise, when a river shrinks to its lower or base-flow state between rainstorms, it moves more slowly than when it completely fills its channel after a rainstorm. The greater its 鈥渉ydraulic radius鈥� 鈥� measured by dividing the cross-sectional area by the wetted perimeter 鈥� the better able the river is to overcome the effect of bed friction.
Big rivers are normally faster than small ones.
Michael Ghirelli
Buckingham
鈥� The velocity of a river can be predicted using Manning鈥檚 equation. This says that the velocity is equal to the square of the cube root of the hydraulic radius, multiplied by the square root of the slope angle, divided by Manning鈥檚 roughness coefficient. The coefficient is a value between 0.02 and 0.03 depending on the terrain and conditions.
As the slope angle and roughness coefficient are constant for any particular part of a river, the hydraulic radius must change to change the velocity. The hydraulic radius is the cross-sectional area of the river divided by the wetted perimeter. As the water level rises, the wetted perimeter varies with the height change, but the change in area is proportional to the square of the height change. Manning鈥檚 equation basically tells us how efficient a channel is. More water means the channel is more efficient because friction is lowered and will flow much faster.
Michael Morley
Torquay, Devon
鈥� I applied the standard Manning open-channel hydraulics formula to the problem. I had to make a number of assumptions but here are my calculations.
Your correspondent probably refers to the Avon in Somerset, close to his home, so I assumed uniform flow in a river 100 metres wide with 1 in 1 sloping banks and a bed slope of 1 in 1000. I first assumed a depth of 1 metre and then a depth of 1.25 metres to simulate a 25 per cent increase in flow. I also assumed a Manning roughness coefficient of 0.03.
I fed this data into a computer program which models simple open-channel flow and outputs the flow per second and the cross-sectional area of the flow. The average velocity is found by dividing the flow by the area, and the calculation indicated an increase from 0.95 metres per second to 1.09. This was an increase of only 14 per cent. Next, I tried an initial depth of 10 centimetres and depth after rain of 12.5 centimetres. The velocity was calculated to increase by 15 per cent, from 0.227 metres per second to 0.263.
The discrepancy is partly explained by the possibility that your correspondent observed the maximum flow in the centre of the river, where the velocity might be double the average. The other explanation is that he was recording an impression of increased velocity rather than an accurate measurement.
Edward Webber
Buckingham
Raising an army
After a friend complained about the overzealous attentions of a lover, I came across a reference in Paul Ferris鈥檚 Sex and the British to the use of bromide in tea as a means of curbing soldiers鈥� sexual appetites. Is this advice I could pass on to my friend? If so, where would I purchase bromide and what dose is recommended?
鈥� In the 19th century, bromide salts were used widely as sedatives to treat everything from epilepsy to sleeplessness. The bromide salts were said to 鈥渞educe the excitability of the brain鈥�. The normal dose was between 5 and 30 grains, which was taken several times a day (there are about 13 grains per gram). In the 19th century it was not uncommon for children of the upper classes to be flattered by the gift of a personal salt cellar for use at meals. They were led to believe this indicated their increasing status within the family group. The salt was in fact mixed with bromide to make the child better behaved.
Mark Wareing
Braintree, Essex
鈥� Bromides are used as a sedative. The libido reduction is really a side-effect. The use of bromide salts as a sleeping draught appears in the novels of Emile Zola, indicating their effects were recognised at some time in the 19th century. In a reference to using bromides to reduce libido, the comic and author Spike Milligan wrote in Rommel? Gunner Who?: 鈥淚 don鈥檛 think the bromide had any lasting effect, the only way to stop a British soldier feeling randy is to load bromide into a 300 lb shell and fire it at him from the waist down.鈥�
John Rowland
Derby
In the 1950s, my service in the Royal Air Force as a national service medic, responsible for pharmacy duties and inspections of mess facilities, led me to conclude that the idea of servicemen鈥檚 tea being laced with bromide was a myth. Nevertheless, there was a strong and widespread belief among recruits during initial training that the apparent loss of male libido must be due to bromide in their tea.
Clive Harris
Cambridge
鈥� I joined the army in late 1945 and remember the suspicion that our tea was laced with bromide. It did taste awful, but most of us, except the very gullible, assumed the story was an 鈥渙ld soldier鈥檚 tale鈥� intended to alarm new recruits. The real reason for our lack of libido was exhaustion brought on by physical training. All we wanted to do was sleep.
David Elliot
London
This week鈥檚 questions
It flies like a bird
Last weekend I bought a helium-filled balloon. Sadly my friend let it go. How high could it climb and how far could it have travelled?
Arthur Newton (age 4)
Cambridge
Old blue eyes
I recently took a photograph of my husband Ally with my terrier Jock. The flash of the camera meant Ally had red eyes when the photo was printed, yet Jock鈥檚 were blue. Why?
Martha McHugh
Glasgow
Foot of God
In view of the recent media coverage of England footballer David Beckham鈥檚 broken foot and the speedy recovery that helped England to their World Cup win over Argentina, which treatments help broken bones heal quickly and how do they work?
K. Negoro
Gainsborough, Lincolnshire