What happens to the respiratory process in a man going up a hill?

As altitude increases, the oxygen level in the atmosphere decreases. Therefore, as a man goes uphill, he gets less oxygen with each breath. This causes the amount of oxygen in the blood to decline. The respiratory rate increases in response to the decrease in the oxygen content of blood. Simultaneously, the rate of heart beat increases to increase the supply of oxygen to blood.

A man going uphill has to exert more effort to climb. This increases the consumption of oxygen. As a result, the partial pressure of oxygen in haemoglobin decreases which creates more demand for oxygen. This is compensated by an increased breathing rate. 

There is a fall of PO₂ level at high altitudes. This lowers alveolar PO₂ and consequently reduces the diffusion of oxygen from the alveolar air to the blood. So oxygenation of blood is decreased progressively. After some time, the affected person gets adjusted to the surroundings due to which the heart rate are accelerated, RBC count in the blood is increased, haemoglobin level and oxygen-carrying capacity are also increased.

When a man going uphill or doing some strenuous exercise then there is more consumption of oxygen. This decreases the partial pressure of oxygen in haemoglobin resulting in more demand of haemoglobin. As a result there is an increased breathing rate to fill the gap.