During drilling of a deep oil well, the drill pipe got rigidly stuck. It was necessary to determine the depth at which the jamming occurred. The engineer ordered the pipe subjected to a large upwards tensile force, i.e., she pulled on it. As a result, the top of the pipe came up due to elastic stretch by 550 mm. At the same time, measurements showed that the pipe elongated by 0.35 mm in a 200 mm gauge length. Determine the depth at which the pipe was stuck. Assume the cross-section of the pipe is constant with depth

Question

During drilling of a deep oil well, the drill pipe got rigidly stuck. It was necessary to determine the depth at which the jamming occurred. The engineer ordered the pipe subjected to a large upwards tensile force, i.e., she pulled on it. As a result, the top of the pipe came up due to elastic stretch by 550 mm. At the same time, measurements showed that the pipe elongated by 0.35 mm in a 200 mm gauge length. Determine the depth at which the pipe was stuck. Assume the cross-section of the pipe is constant with depth

Answer 1

Here is my solution for the above problem.

Rate of strain = 0.35/200 = 1.75x10e-3

Since no external force is applied rate of strain will be same for entire length.

Let's assume depth of clay as L

then,
extension/Total length of pipe = rate of strain

500 mm / L = 1.75x10e-3

Hence L = 285.7 m.

Depth of clay = Length of pipe + height of derrick.

Answer 2

To determine the depth at which the pipe got stuck, we can use the concept of strain and the relationship between strain and elongation.

Strain (ε) is defined as the change in length (ΔL) divided by the original length (L). In this case, the strain can be calculated as:

ε = ΔL / L

Given that the pipe elongated by 0.35 mm in a 200 mm gauge length, we can substitute these values into the formula:

ε = 0.35 mm / 200 mm

Now, let's determine the strain for the entire pipe using the given information. The top of the pipe came up by 550 mm due to the tensile force applied. Since the pipe's cross-section is constant with depth, the strain is the same throughout the pipe.

So, the strain for the entire pipe can be calculated as:

ε_total = 550 mm / original length (L)

Now, we can equate the two strain values and solve for the original length of the pipe (L):

0.35 mm / 200 mm = 550 mm / L

Cross-multiplying and rearranging the equation, we have:

L * 0.35 mm = 200 mm * 550 mm

L = (200 mm * 550 mm) / 0.35 mm

Now, we can determine the depth at which the pipe got stuck. Since the top of the pipe came up by 550 mm and the original length was L, the depth at which the pipe got stuck is:

Depth = original length (L) - 550 mm

Substituting the value of L we just calculated, we can find the depth at which the pipe got stuck.