Well let's work this out.

Assuming a fully developed flow in a pipe, the pressure drop (DP) can be written as follows:

DP = (f*rho*L*U^2)/(2D)             (1)

where:

f = darcy friction factor

rho = fluid density

L = pipe length

U = average fluid velocity across the pipe

D = pipe diameter

It is more convenient to re-write U^2 in the above equation in terms of the mass flow rate:

m_dot = rho*U*(pi*D^2/4)

So,

U = 4*m_dot / (rho * pi * D^2)

U^2 = 16*m_dot^2/(rho^2 * pi^2 * D^4)

Plugging this expression of U^2 into Equation (1) yields the following:

DP = (8*f*L / (rho *pi^2 * D^5))* m_dot^2

For a fixed m_dot, you can easily work out what the pressure drop is as a function of friction factor and density of the two fluids.

Sir, 

To my knowledge, Water and Super heated steam can not co-exist.  By definition, if water is present in steam it will be called wet steam and steam must be dry to get super heated.  

Let me assume that you are mixing the two fluids, may be, for some numerical analysis purpose, then the mixture should be at the same saturated temperature corresponding to a specific pressure.  

If my assumption is correct, then, the approximate volume of 1 kg of water is nearly one liter and that for steam is nearly 1.6.m**2.  As you have mentioned the mass flow rates are the same; due to the large difference in specific volumes of the two phases, the velocity of steam should be too high in comparison to water.  Possibly, the flow pattern could be annular flow.  You can refer to M.M.Shah and his graphical methods of estimating drop in pressure (dp).  He has used hundreds of fluid / test fluid combinations in the analysis.  It may solve your problem to a large extent.   

Moreover, any instrument to measure dp, may provide you an average value of the total pressure drop, but not the dp of each phase.  May be there is a software to do this.  

Wish you all the best in your research.  

Dr.S.Ravindran

Sir, Thanks for the answer. I was referring to the flow of water and super heated steam in 2 separate tubes or ducts with same restrictions in the pipe network and same mass flow rate.

I hope that Firas Siala has answered you in this regard

Dr. S. Ravindran

Yes, Firas Siala has shown the equations to estimate pressure drop for fluid in a pipe.  One might also expect the pressure drop to be a function of viscosity which is it through the friction factor which relates Reynold's number and surface roughness to friction loss.  Another issue not mentioned above is that the mechanical energy equation (Bernoulli's Equation) is applicable for incompressible flows.  Liquid water fits this criteria but super heated steam may not (depending on the flow velocity). Thus, the equations used by Firas Siala to demonstrate the relationship between pressure drop, fluid density and friction factor may not be completely accurate as given.

Joseph Smith is correct. I was thinking of Air, which is assumed to incompressible. 

Refer to Two-Phase Flow, Boiling, and Condensation textbook by Ghiaasiaan. 

pressure difference is directly proportional to density and Viscosity. Water have high density as compared to steam.if you are use mixture then we have to identify the fraction of water in mixture.

Pressure drop in fluids depends on density and viscosity. 

Isn't it pressure drop is more for fluid having higher kinematic viscosity?

good question, and will make no calculation; gas being 1000 times lighter than liquid, same mass flow means 1000 higher speed, and as pressure drop is proportional to speed to the square, it means 1 million more pressure drop than with a gas at going at the same speed as the liquid.

Thank you sir.

I wanted to the know the answer of another question...

What is the effect of pressure on heat transfer characteristics of water? 

If pressure of hot  water flowing through tubes is increased, what effect it will have on the heat transfer from this hot fluid to the cold fluid to which it is supposed to dissipate heat.

Water is an incompressible fluid therefore pressure doesn't affect density and has a very negligible affect on viscosity thus the Reynold's number isn't affected.  The heat transfer coefficients are normally functions of Reynold's number and Prandtl number:

Nu = hD/k = A*Rea * B*Prb

The only effect pressure might have on heat transfer would be by increasing the fluid flow inside the tubes thus increasing the Reynold's number:

Re = D*V*rho/vis

which indicates increased fluid mixing inside the tube.

Pressure increment mean mass flow rate is increased.

Analysis is based on enclosed figure.

It's clear that increased mass flow bring more heat into the flowing stream.

If T_s is fixed: Heat transfer rate (to cooler fluid) will be increased.

If q_s is fixed: Increased mass flow rate keep heat with flowing stream.

Conclusion: Depend of the scenario you have, choose the answer.

Dear Ashok Singh,

I am not getting how with increase in pressure mass flow rate increases