To calculate the velocity distribution of particles hitting this small area, we must take into account that all the particles with ( v , θ θ , ϕ ϕ ) that hit the area d A within the time interval d t are contained in the tilted pipe with a height of v cos ⁡ ⁡ ( θ θ ) d t and a volume of v cos ⁡ ⁡ ( θ θ ) d A d t ; Therefore, compared to the Maxwell distribution, the velocity distribution will have an extra factor of v cos ⁡ ⁡ θ θ : f ( v , θ θ , ϕ ϕ ) d v d θ θ d ϕ ϕ = λ λ v cos ⁡ ⁡ θ θ × × ( m 2 π π k T ) 3 / 2 e − − m v 2 2 k B T ( v 2 sin ⁡ ⁡ θ θ d v d θ θ d ϕ ϕ ) with the constraint v > 0 , 0 < θ θ < π π 2 , 0 < ϕ ϕ < 2 π π . The constant λ λ can be determined by the normalization condition ∫ ∫ f ( v , θ θ , ϕ ϕ ) d v d θ θ d ϕ ϕ = 1 to be 4 / v ¯ ¯ , and overall: f ( v , θ θ , ϕ ϕ ) d v d θ θ d ϕ ϕ = 1 2 π π ( m k B T ) 2 e − − m v 2 2 k B T ( v 3 sin ⁡ ⁡ θ θ cos ⁡ ⁡ θ θ d v d θ θ d ϕ ϕ ) ; v > 0 , 0 < θ θ < π π 2 , 0 < ϕ ϕ < 2 π π