Apples are not only a foodstuff, but also a raw material for many industrial production fields, and the market demand is constantly increasing. The Loess Plateau is one of the world’s largest apple-producing areas, with about 85% are aged orchards (more than 20 years old), facing problems such as poor soil water retention, degradation of tree strength, and declining yield and quality, etc., so do aged orchards in other regions of the world, and study on improving quality and increasing yield of aged orchards is of great significance to the sustainable development of the apple industry. Here, 6 treatments (2, 4, 6, 8, 10 and 12 kg/plant) were designed in the experiment to study the effects of biochar on yield and quality in aged apple orchards. The study showed that: biochar could improve soil water retention, but caused the soil alkalization; biochar could improve apple quality and increase yield, T3 and T4 were of better quality, and T3 had the highest yield. Comprehensive analysis, T3 is the optimal scheme. The results not only provide a reference for aged orchards worldwide, but also have great significance for the sustainable development of the apple industry.

The drag and lift coefficients are important parameters that affect the particle motion in a viscous fluid. In the present study, the drag and lift coefficients of a spinning sphere in a water tank were studied experimentally using a high-speed camera. To this end, 22 cases were studied to cover a wide range of dimensionless angular speeds (0.149 < Rr < 3.471) and Reynolds numbers (610 < Re < 3472). Based on the present experimental data and the results obtained from the literature, expressions were developed to calculate the lift and drag coefficients. The performed analyses on lift coefficient show that there is a critical Reynolds number (Re_c) at each dimensionless angular speed. When 0 < Re < Re_c, the lift coefficient decreases with increasing the Reynolds number, while it is constant when Re_c < Re< 3500. The constant lift coefficient corresponding to different spin speeds was defined as the limit value of the lift coefficient. It is found that when 1 < Rr < 12, the limit value of the lift coefficient is 0.37, while the limit value of the lift coefficient increases with increasing dimensionless angular speed at 0 < Rr < 1. It is found that the spin increases the drag coefficient of a spinning sphere only when 0 < Rr < 10. Moreover, the performed analyses show that the drag coefficient of a spinning sphere is less than that of a non-spinning sphere when 10 < Rr < 25. Furthermore, the lift-to-drag ratio of a spinning sphere is discussed in this article.

The drag coefficient plays a dominant role in the particle motion. The main objective of the present study is to extract a mathematical correlation between the total drag coefficient and the particle motion parameters. To this end, the total drag coefficient of a sphere with a variable velocity in a water tank was studied experimentally using a high-speed camera. An expression was developed to simulate the correlation between the total drag coefficient, the Reynolds number, and the acceleration coefficient. Then the developed expression for calculating the total drag coefficient based on the Reynolds number was improved. Moreover, the correlation between the Froude number and the acceleration coefficient was analyzed and an expression was developed in this regard. A formula for calculating the total coefficient based on the Froude number was established. The obtained results show that the total drag coefficient has a complex change with an increasing Reynolds number at a determined acceleration coefficient. Furthermore, it is found that at a constant Reynolds number, the total drag coefficient decreases as the acceleration coefficient increases. The performed analyses demonstrated that the established expression based on the Froude number has high accuracy and low computational complexity.