When fluid will pass through a pipe, if we want to measure the fluid's properties from the vibration will the dia of pipe will effect its vibration?

We have a one meter long copper pipe through which water passes at a certain speed. The outer wall of the tube is covered by the heater where all the energy of the heater is transferred to the tube. Now the outer wall of the tube is vibrated in a vertical direction by a vibrator using different frequencies up to 3000 Hz. We want to examine the rate of heat transfer at each of the vibrational frequencies at the end of the fluid.

I am trying to model a process in which there is a flow of non-newtonian Herschel-Bulkley fluid. to derive equations of pressure drop, wall shear stress and drag force(for spheres inside the fluid) i need a form of reynolds number for herschel bulkley fluids.reynolds number should consider existence of yield stress in rheogram of fluid.

so is there any generalized form of Reynolds number that is applicable for herschel-Bulkley fluids??

I surveyed previous works but i didn't finds so much about

What happens to the natural frequencies of a fluid conveying pipe if an intermediate support is present?

Please share any supporting material with me if you have it.

Can we convey hot fluids using reinforced concrete pipes?

I have a pipe with 10 mm in Diameter and 2 bar pressure, the fluid velocity is 200 m/s, the fluid is air.

is there a way to reduce velocity without affecting the pressure value?

Frictional Head loss calculated by input velocity of the fluid flow, the density of the fluid, the orientation of the pipe system (how many bends, whether the bend is horizontal or vertical).

my understanding is that head loss in a pipe depends on flow so suppose in a pipe i have calculated that 1kg/cm2 is head loss at 100 ltr/hr flow .

Case 1 - i put a pump at staring end which will put 100 ltr/hr flow in this pipe at initial pressure of 4kg/cm2 then i conclude that at outlet i will get 100ltr/hr flow at 3 kg/cm2.

Case 2 - i put a pump at staring end which will put 100 ltr/hr flow in this pipe at initial pressure of 6/cm2 then i conclude that at outlet i will get 100ltr/hr flow at 5 kg/cm2.

Do you think my conclusions are correct

Bernoulli equation is very well-known equation and is very often used to analyze and design piping systems. But we know that in this equation there are at least 4 assumptions applied, namely: 1) fluid is inviscid 2) fluid is incompressible; 3) applies to a streamline; 3) no energy enters or exits;.

Your comments are very appreciated.

Regards,

Nazaruddin Sinaga

In his book: "FUNDAMENTAL PRINCIPLES OF POLYMERIC MATERIALS", Third Edition, 2012, Wiley, the authors Brazel & Rosen wrote, page 274, problem 14.18: "Note: The fluid is pseudoplastic, but not power law.". What is the key to explain it? I know that there is Non-newtonian fluids, like Bingham, Casson, Herschel-Bulkley with yield stress value, which can not be described by power-law (Ostwald de-Waelle) model. I also know about Cross, Carreau, and other rheological models, with zero shear viscosity, infinite shear viscosity, etc. But, in the context of the problem proposed by the authors, what is the limitation, or, in other words: what is the implication of a fluid that is shear thinning (at least in some intermediate region of shear rate), but that cannot be described by the power-law model? What difference does this make to pipe sizing to ensure laminar flow?