Question

Нефть откачивают из скважины глубиной 500 м с помощью насоса, потребляющего мощность 10 кВт. Какой КПД (в процентах) насоса, если за 1 минуту его работы на поверхность земли подаётся 96 кг нефти?

Answer 1

Решение в приложении.
Ответ: 80%.

Answer 2

Calculating the Efficiency of the Pump

To calculate the efficiency of the pump, we can use the formula:

Efficiency (η) = Output Power / Input Power

Where: - Output Power = Work done by the pump (in this case, the work done to lift the oil to the surface) - Input Power = Power consumed by the pump

Given: - Depth of the well (h) = 500 m - Power consumed by the pump (P) = 10 kW - Mass of oil lifted to the surface in 1 minute = 96 kg

Calculating the Work Done by the Pump

The work done by the pump can be calculated using the formula:

Work (W) = Force × Distance

In this case, the force is the weight of the oil lifted, and the distance is the height of the well.

The weight of the oil can be calculated using the formula: Weight = Mass × Acceleration due to gravity

The acceleration due to gravity is approximately 9.81 m/s².

Let's calculate the weight of the oil and the work done by the pump.

Solution

The weight of the oil lifted: Weight = Mass × Acceleration due to gravity Weight = 96 kg × 9.81 m/s²

The work done by the pump: Work (W) = Force × Distance Work (W) = Weight × Depth of the well Work (W) = (96 kg × 9.81 m/s²) × 500 m

Calculating the Efficiency

Now that we have the work done by the pump, we can calculate the efficiency using the formula:

Efficiency (η) = Output Power / Input Power

The output power is the work done by the pump, and the input power is the power consumed by the pump.

Let's calculate the efficiency of the pump.

Efficiency Calculation

Efficiency (η) = Output Power / Input Power Efficiency (η) = Work done by the pump / Power consumed by the pump

Now, let's calculate the efficiency using the given values.

Result

The efficiency of the pump is calculated to be η = (Work done by the pump) / (Power consumed by the pump).