# Just some simple fluid mechanics questions

bernoulli's principle says..
total pressure = static pressure + dynamic pressure + pressure from height, right?

but how come I hear that an increase in velocity is a decrease in pressure? if you increase velocity as the 'v' part in dynamic pressure won't the entire pressure increase as well? because it just adds to the rest. Same thing with height pressure. if height is higher, won't the total pressure be more because you mutiply height to gravity and density, then you add to other pressures.

I read as an example on a site... that when you turn on the shower in the bath tub the curtains get pulled inward beacuse of a decrease in pressure ( . )

Well if it starts raining outside then, does this mean atmospheric pressure is no longer 14.7psi, but less?

this is confusing. plz clarify, thanks.

## Answers and Replies

dextercioby
Homework Helper
The total pressure must be the same,that's why you're using that formula due to Daniel Bernoulli.That's why static pressure must drop,once the dynamical one incresed.

Daniel.

Q_Goest
Homework Helper
Gold Member
The increase in velocity = decrease in pressure statement is in reference to a given flow stream, not different ones. In other words, given a flow stream where velocity is X, if that flow stream were to be reduced in area, then velocity would increase. And if velocity increases in that flow stream, then the static pressure decreases.

You are correct that given the equation, if the static and head pressure stays constant, and one simply increases the velocity, then the total pressure is higher. But note that if this is the case, when you increase velocity, the flow rate must also increase. So you're comparing two flow streams, one has more flow than the other.

Regarding the shower curtain, someone's messing with your mind. I believe that has to do with warming the air inside the shower, the warm air is more bouyant, and cold air wants to get in at the bottom, which pushes the shower curtain in. That's a thermal effect, not a mechanical one.

Doc Al
Mentor
shower curtains

Q_Goest said:
Regarding the shower curtain, someone's messing with your mind. I believe that has to do with warming the air inside the shower, the warm air is more bouyant, and cold air wants to get in at the bottom, which pushes the shower curtain in. That's a thermal effect, not a mechanical one.
I don't believe it's a thermal effect: try it with cold water. Up until a few years ago, I would have said that the reason for the shower curtain sucking inward was the Coanda effect and viscosity--the same effect that causes a piece of paper to rise when you blow over it. (This "blowing across the paper" demo is usually meant to demonstrate Bernoulli; but it doesn't.) But a few years ago someone at the University of Massachusetts actually did a mathematical model of the problem and found that the main thing going on was that a vortex is created in the shower: the resulting low pressure pulls the curtain inward. (I don't know the details of his model.)

arildno
Homework Helper
Gold Member
Dearly Missed
Just to make it clear about the Bernoulli principle:
This derives a relation VALID ON A STREAMLINE.
Since we also need STATIONARY CONDITIONS in order to use (the usual) Bernoulli, it follows that Bernoulli equally well can be said to relate the energy for the SAME fluid particle at two distinct points on its trajectory (since the particle trajectory will coincide with the streamline in the stationary case).

Now, if the particle has a greater speed at some point of its trajectory, it has necessarily experienced a tangential acceleration.
But, (ignoring change in gravitational potential for simplicity), if a fluid particle is to accelerate along its trajectory, then the pressure at the point where it has lowest velocity must be greater than the pressure value at the point where it accelerates to...

ohh... so the statement "increase in velocity results in decrease in pressure" refers to the static pressure of the fluid, not the total? is static pressure just commonly refered to as just "pressure" or something? or am i still mistaken?

so increase in velocity will increase the dynamic pressure of a fluid but in turn, the static pressure MUST decrease? what if it doesn't?

thanks guys.