The drilling engineer's problem

A borehole is filled with mud with a mud weight of 1,200kg/m3. All of the immersed equipment is made of steel with a mass density of 7,800kg/m3.

The well is drilled using a 27cm diameter drill bit, 30cm high and with a mass of 68kg.

The drill bit is attached to the lower end of a drill string consisting successively, from bottom to top, of :

• a coupling 1m long, 20.3cm outside diameter and 7.7cm inside diameter,
• 14 drill collars, each 9.144m long and with the same internal and external diameters as the coupling,
• a string of 354 pipes each 9.144m long, weighing 265kg each.

How much upward force (F₁) is needed on this drill string so that the pressure exerted by the drill bit at the bottom of the well does not exceed P₁=3.6.10⁶ Pa?

Where g is constant and equal to 9.81m/s2.
All of the equipment is assumed to be immerse in mud.

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See the next edition of odyssey for the explanation.