According to Bernoulli's equation, an increase in velocity should be associated with a decrease in pressure. Yet, when you put your hand outside the window of a moving car, increasing the speed at which the air flows by, you sense an increase in pressure. Why is this not a violation of Bernoulli's equation?

According to Bernoulli’s equation, the total energy of the flow of fluid remains constant. It is true when the flow is steady or laminar. The consequence of this equation is that the increase in the pressure of the flow of fluid is accompanied by the decrease in speed of the flow of fluid and vice versa.
The flow of air near the window of the moving car is not laminar. It is turbulent near the car due to the shape of the car. So, Bernoulli’s equation cannot be applied here. So, the increase in velocity of the air is not associated with the decrease in pressure. Thus, it is not a violation of Bernoulli’s equation. The result is that we feel an increase in pressure when we put our hand outside the window.