Why is there a relationship between speed and pressure? What is that relation? Why are they inverses of each other?

When a fluid is flowing smoothly and steadily through a stationary environment, its energy is conserved. As long as it doesn’t lose much energy to frictional effects, you can count on its total energy remaining essentially constant as it flows downstream. Since it only has three forms for its energy: gravitational potential energy, pressure potential energy, and kinetic energy, you can expect that a decrease in one of these forms of energy will be accompanied by an increase in one of the other forms. That’s when speed and pressure are inversely related. When the fluid slows down, its kinetic energy drops so its pressure potential energy (and its pressure) must rise.

Why is it that when I am in my dorm room with my window open and the door closed, there isn’t a change in temperature and no wind comes in or blows around. But if I open the door, the room becomes cold and wind is felt throughout the room?

When the wind blows into your room, it comes to a stop and experiences a rise in pressure. This is an consequence of Bernoulli’s equation, which recognizes that energy is conserved and that in a fluid, energy can exist either as kinetic energy (energy of motion), pressure energy, or gravitational potential energy. In this case, the wind’s kinetic energy becomes pressure energy as it slow down in your room. As the pressure in your room rises, it prevents more air from entering, so you have high pressure but no movement inside your room. As soon as you open the door, the high-pressure air in your room accelerates toward the relatively low-pressure air in your hall. The pressure in your room drops and the wind can get in now. Soon the wind is blowing right through your room, as though you were part of a wind tunnel. If the wind is cold, you will be too.

Why is high pressure air/fluids slow moving, while low-pressure fluids/air are fast moving?

First, I should point out that high pressure air/fluids can move either fast or slow, depending on the situation. The same holds for low-pressure air/fluids. What Bernoulli’s equation tells us is that when air/fluids slows down, its pressure rises (assuming that it isn’t moving up or down so that gravity is out of the picture) and when air/fluids speed up, its pressure drops. Here are two common examples.

First, when you spray water from a garden hose against your hand, the water goes from moving quickly through the air at atmospheric pressure to moving slowly on your hand at more than atmospheric pressure. You know that this pressure increase has occurred because you feel the water pushing hard on your hand. The water is exchanging kinetic energy for pressure potential energy and its pressure is rising.

Second, when you put your thumb over the end of the garden hose and allow only a fine spray to emerge, the water goes from slow moving water at high pressure inside the hose to fast moving water at atmospheric pressure in the air. You know that this pressure drop has occurred because you feel the water in the hose pushing hard against your thumb. The water is exchanging pressure potential energy for kinetic energy and its pressure is dropping.

Why does water stay in the straw when a finger is pressed over one end? How does sealing off the one end make the pressure less?

When you fill a straw with water and then seal one end with your finger, you can then hold the straw vertically without any water falling out of the straw. That’s because the air pressure above the column of water decreases until the upward force caused by the unbalanced pressure at the top and bottom of the water column is exactly equal to the weight of the water column. The drop in pressure above the water column occurs because the water initial does fall downward. When you first tip the straw from horizontal to vertical, the air pressures above and below the water column are equal and there is no pressure force to opposite the weight of the water. The water begins to fall. As it does, it creates a relatively empty region above the water column and below your finger. The air molecules in that region become sparser and their pressure decreases as a result. The water descends just far enough to lower the pressure inside that trapped air region until the pressure force balances the water’s weight. Actually, the water column bounces up and down briefly, just like a weight at the end of a spring or a person at the end of a bungee cord. But after a second or so, the water column just hangs there motionless in the straw, supported against gravity by the pressure imbalance. If air could work its way through the water column and enter the trapped region between the water column and your finger, the water column would be able to descend further. But the straw is so narrow and the water sticks to tightly to itself (a phenomenon called surface tension) that it prevents air bubbles from working their way up the straw.