Recent Updates

VELOCITY OF SOUND IN TERMS OF BULK MODULUS

Till now we were discussing the various concepts and equations such as continuity equationEuler equationBernoulli’s equation and momentum equation for incompressible fluid flow. In same way we have also discussed above equations for compressible fluid flow. 

We have already seen the derivation of continuity equationBernoulli’s equation and momentum equation for compressible fluid flow in our previous posts. We will start here our discussion about the compressible fluid flow with the derivation of expression for velocity of sound in terms of bulk modulus. 

Expression for velocity of sound in terms of bulk modulus 
Before understanding the process to derive the expression for velocity of sound in terms of bulk modulus, we must have to study our previous post which shows the derivation of velocity of sound wave in a fluid

As we are interested here to find the expression for velocity of sound in terms of bulk modulus, therefore let us brief here first the term bulk modulus. 

Bulk modulus of elasticity of a substance is basically defined as the ratio of compressive stress or hydro static stress to volumetric strain and it will be displayed by the symbol K. 

Bulk modulus of a substance provides the information about the resistance of substance to the uniform pressure. In simple, we can also say that Bulk modulus of a substance provides the information about the compressibility of that substance. 

Bulk modulus, K = - dP/ (dV/V) 

Where, 
dP = Change in pressure 
dV/V = Volumetric strain 

As we know that according to the conservation of mass, we will have following equation as mentioned here. 

Density x Volume = Constant 
ρ x V = C, where C is constant 

Let us differentiate the above equation and we will have following equation after differentiation 

d (ρ x V) = 0 
ρ d V + V dρ = 0 
ρ d V = - V dρ 
dV/V = -(dρ/ ρ) 

Now we will use the above value of volumetric strain in equation of bulk modulus and we will have 

K = ρ x dP/dρ 
dP/dρ = K/ ρ 

Let us recall the expression for the velocity of sound wave in a fluid and we can write the above equation as mentioned here. 

C2 = K/ ρ 

Because, 
dP/dρ = C2
Where, C is the velocity of sound 

Therefore we will have following equation, as mentioned here, which shows the expression for velocity of sound in terms of bulk modulus. 

Further we will go ahead to find out the expression for velocity of sound in isothermal process, in the subject of fluid mechanics, with the help of our next post. 

Do you have any suggestions? Please write in comment box. 

Reference: 

Fluid mechanics, By R. K. Bansal 
Image courtesy: Google 

Also read  

8 comments:

  1. I got too much interesting stuff on your blog. I guess I am not the only one having all the enjoyment here! Keep up the good work. hypnosis subliminal downloads

    ReplyDelete
  2. Begin by marking in to your Google record and explore to your YouTube channel page, then, at that point at the highest point of your channel page, click on perspectives to go straightforwardly to your channel's investigation. yt mp3 converter

    ReplyDelete
  3. -家庭劇院系統 / 多聲道環繞音效層次感、逼真度、震撼力是劇院的基本關鍵,讓您在家不管是在聽最愛的那首歌,還是在看電影,就可以置身於情境當中,視覺聽覺同時滿足到靈魂深處。 音響店

    ReplyDelete
  4. Thanks for every other informative site. The place else may just I get that kind of information written in such an ideal means? I have a venture that I’m just now operating on, and I have been on the look out for such information. Sales velocity calculation

    ReplyDelete
  5. This article provided me with a wealth of information about Magnetic coupling. The article is incredibly helpful and offers some of the most useful information. Thank you for sharing it with us.

    ReplyDelete
  6. It is what I was searching for is really informative.linear motors, It is a significant and useful article for us. Thankful to you for sharing an article like this.

    ReplyDelete
  7. Also, there are some acceptable ones out there as well! I'm simply more knowing with regards to where I invest my energy and cash now and I quit pursuing the following sparkly proposition." Magnetic core material.

    ReplyDelete