Question

An oil gusher shoots crude oil 25.0 m into the air through a pipe with a 0.100-m diameter. Neglecting air resistance but not the resistance of the pipe, and assuming laminar flow, calculate the gauge pressure at the entrance of the 50.0-m-long vertical pipe. Take the density of the oil to be (900 kg/m^3) and its viscosity to be (1.00 (N/m^2).s) (or (1.00 Pa.s)). Note that you must take into account the pressure due to the 50.0-m column of oil in the pipe.

(a) Calculate the gauge pressure.
a) (9.80 Pa)
b) (196 Pa)
c) (392 Pa)
d) (784 Pa)

Answer 1

To calculate the gauge pressure at the entrance of the pipe carrying oil, both the hydrostatic pressure from the oil column and the resistance of the pipe should be considered. However, the calculation is incomplete due to the lack of flow rate information needed for the Hagen-Poiseuille equation.

Step-by-step explanation:

The question asks us to calculate the gauge pressure at the entrance of a 50.0-m-long vertical pipe through which oil is shooting 25.0 m into the air. To solve for the gauge pressure, we must consider the weight of the oil column and the resistance of the pipe due to viscosity.

First, we can calculate the pressure due to the weight of the oil column, which is given by P = hρg, where h is the height of the column, ρ is the density of the oil, and g is the acceleration due to gravity. Plugging in the numbers, we get:

P = 50.0 m × 900 kg/m³ × 9.81 m/s² = 441450 Pa

Next, knowing that the flow is laminar, we can use the Hagen-Poiseuille equation to find the additional pressure needed to overcome the resistance of the pipe. However, to use this equation, we need the flow rate, which is not provided in the question. Without the flow rate, we cannot proceed with this calculation.

Thus, based on the provided information, we can only determine the pressure due to the oil column. This partial calculation would not be the final answer to the question but is only an intermediate step.