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Some Don’t like It Hot

Hot water is flowing through an unbreakable, unbendable, opaque and infinitely long metal pipe.

Published: 16th December 2018 05:00 AM  |   Last Updated: 13th December 2018 09:50 PM   |  A+A-

....unless it is winter!

Hot water is flowing through an unbreakable, unbendable, opaque and infinitely long metal pipe. How do you find out in which direction it’s flowing?” Please note that answers utilising ultrasonic flow meter technology are way too technical and expensive and that money would be far better spent sending it to me instead.

THROUGHPUT
(The problem was: “what kind of surface would make a vehicle with square wheels ride smoothly?”)
As the square wheel rolls across a flat surface, the centre of the square changes elevation. To compensate for these elevation changes and to smooth the ride, the surface of the road needs to be uneven. A series of these “bumps” forms a road that a square wheel can roll smoothly on.

To determine the shape of these ‘bumps’, the design criteria is that (1) the centre of the wheel must stay at a constant height ‘d’; (2) the wheel must be tangent to the road’s surface at the point of contact; (3) the centre of the wheel should be directly above the point of contact with the road’s surface; (4) the distance along the surface of the bump must be equal to the length of one side of the square. An uneven road surface built with the above design criteria would make a vehicle with square wheels ride smoothly. -- Narayana Murty Karri, k_n_murty@yahoo.com

To make the ride smooth, the surface of the road should be designed to keep the height of the axle from the road constant during each rotation of the wheel and also to stop the wheel from dropping from its heighest position perched on the corner of the square to a side. This is achieved by giving the road an undulating surface whose cross section along the length is the locus of the axle of a square wheel moving on a flat level surface. The surface will be made up of blah blah blah and the wheel moves smoothly over the curved surface of the road and doesn’t drop in a jarring way. -- Balagopalan Nair K, balagopalannair@gmail.com

I know the answer without Googling because the practical set up is present in the Vishveswaraya Museum Bengaluru. -- Ganesh Ram Palanisamy, 1969ganram@gmail.com (I don’t know . . . is this cheating or what? -- MS)(The second one was: “The planets of our solar system are such that if you replace the alphabet of five of them by numbers zero though nine then the sum of them is equal to the fifth one. Name these planets and find the number denoting each alphabet. (Earth is not considered and no leading zeros are allowed.”)

(1)  My ten-year-young daughter got me to solve this BGTN first thing on this cool Sunday morning. Explaining to her, the first step was to ‘find’ five planets which have only ten alphabets in them. These planets are: VENUS, MARS, SATURN, URANUS, NEPTUNE. (2) Since NEPTUNE has the longest spelling amongst these, it is the sum (solution) of the other four. (3) Solving for MARS + VENUS + SATURN + URANUS = NEPTUNE, gives the solution 4593 + 20163 + 358691 + 695163 = 1078610. Voila! -- Charanjit Singh Pardesi, cspardesi@gmail.com

(Some fan mail was apparently left out so let’s get them back on board again.)
These two were too straightforward and I could not resist sending short solutions. (1) In winter, ceiling fans should rotate clockwise at a low speed to enable pulling cool air up. The gentle updraft pushes warm air, which naturally rises to the ceiling, down along the walls and back the floor.

This makes a room feel warmer. However, this does not work if your ceiling (and hence the fan) is very high - for example, in a cathedral. (2) The source of the bleed air (compressed air that enters the turbine) is very very cold (-30 C) when the plane is flying. The air conditioning unit has been adjusted for the same. When the plane is on the ground, the source air is much warmer (hint: “grass is present in Bakustrade”) and resultant air-conditioning is not very comfortable for folks sitting inside in the plane. Keep doing the good work to tickle our brains every week! --Anand Sinha, sinha.anand.iim@gmail.com

BUT GOOGLE THIS NOW
In the film Gandhi, the Mahatma seeing a poor ill-clad woman sitting downriver from him, takes off his chaadar, crumples it and throws it into the water. As it floats towards her the chaadar stretches out on the water. What makes it open out in such a manner?
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)

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