Bernoulli Equation Derivation

[@LearnChemE]

We can rewrite the term V* dV/ds as the right side = 1/2 d(V^2)/ds, so we plugged the right side into the equation above it. This removes the floating V before the differential.

[@LearnChemE]

Since we are talking about motion along the streamline, we are only concerned with the pressure that acts as a force in the direction of motion. However, you are right in that we need to consider the n(y) pressure (hydrostatic pressure) as well.

[@LearnChemE]

The density can vary throughout the flow field, thus for compressible fluids it becomes a function of pressure and you would treat it as such. But for the derivation here, we are looking at a differential fluid element, where we say the mass is equal to some differential volume * density. We are not taking a set volume * some differential density.

[@LearnChemE]

By definition of velocity in the s-direction, ds/dt = velocity (V).

[@Icetorm]

Of course! Thank you for your reply.

[@i7love7football]

Nice derivation, thank you!

[@papayaday3912]

Very clear explanation! Thank you sir

[@sergeydukman5832]

Too few views for this video. Very well explained

[@louistkach4547]

You state: dn=0 when considering motion along a streamline. is that saying the motion is rectilinear? n is constant. dn=0. This n = negative of radius of curvature. So here that radius of curvature is a constant?

[@Icetorm]

Out of interest, wouldn't the pressure be a function of n and y, not s and n? It's the surface area dn*dy that makes the difference in pressure? Thank you

[@JoystuckTV]

On 2:10 - when we represent mass as rho*dV - don't we have to put rho under the differential sign? That can be valid for incompressible, but for compressible fluids density is variant, so needs to be treated like such, i,e, taken with a differential. Ain't I right?

[@sussybaka3420]

It’s infinitesimal so you can treat it as uniform density

[@benny...solution2321]

Nice has been done it simplify studies

[@TheBetadecay]

How does V= ds/dt? If fluid flow is in a straight line doesn't ds/dt=0, but not V?

[@yessimzhanraiymbekov3564]

Should the weigth term consist of gravitational canstant g? If it not why the direction ?

[@winner1338]

Tetha is changed? at 2:45 between dn and vertical at 5:22 between ds and horizotal please explain

[@MultiPapayaman]

hello, I am confused as to why the two pressure forces acting opposite to each other. Can anyone please tell me why?

[@subratkumar2762]

FranciscoLorenzo PHD here we are considering the small volume of fluid chunk as the system and analyzing the forces acting on it.As to why they are opposite to eachother , it can be easily understood through NEWWTON'S 3RD LAW

[@fMalhota1]

at 4:46 you multiply a weight and a force? I do not understand why you do not multiply the weight by the gravitation? - Thanks hope you can help me understand.

[@LearnChemE]

Sorry, that is a plus sign, not a multiplication sign.

[@fMalhota1]

LearnChemE Sorry, that is what i meant - how can you plus a weight and a force - when you want to find the force of gravity you does not multiply the weight with the gravitational acceleration. Thank you for your time.

[@LearnChemE]

Weight is a force. You are taking the mass and multiplying it by acceleration due to gravity. In this case we are taking the specific weight (density * gravity) and multiplying it by the differential volume to get our differential mass * gravity. The sin term accounts for the direction in the y-axis.

[@fMalhota1]

Tankyou for your help!

[@LearnChemE]

Of course! Thanks for using these.

[@MH-oc4de]

Wow, where is the guy who did the Navier Stokes derivation ? This lecture was downright awful.

[@danielrobles4884]

4:36, what happens to the negative and how does it simplify to that?!

[@screenflicker1]

Bernoulli equation needs to start with stating of Bernoulli principle.

[@TejSwaroop]

someone, please clarify me 6:11 :) thanks