Ram has two identical tanks, one filled with water and the other with mustard oil. The tanks have outlets at the bottom, as shown, which was initially closed. Now Ram opens both the outlets simultaneously.
Which tank is going to be emptied first?
Assume laminar flow of liquids.
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Water is more viscous than gasoline
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But the question asks about petrol. Coefficient of viscosity for petrol is 0.0002 but that of water is 0.0001
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Petrol=gasoline. What is your source? The link I shared has water at 0.01 but gasoline as 0.006 Poise
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@Jeremy Galvagni – I have seen it in a problem that viscosity of petrol is 0.002
how about petrol is less density than water?
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The density doesn't matter: as for a stone, the heaviest doesn't fall faster.
Are you sure that water is less viscous than petrol? Where did you find these values?
If there is no friction then there is no shear, strain rate, viscous dissipation; in the absence of friction all fluids are inviscid. The correct answer to this question as stated is the same time.
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I edited the question afterwards thinking that the answer will be correct only if friction is absent.
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You didn't go quite far enough. The tank surfaces must have friction as well in order for the fluid to resist flow. It is necessary in viscous flows that a no-slip boundary condition is present ( the fluid velocity is zero at the boundary where the fluid meets the other surface) This requires that there is friction between the fluid and conduit. Imagine a frictionless incline. Put a drop of molasses and a drop of water on it. Which is going to hit the bottom of the incline first? The viscosity of the molasses is rendered useless in in the absence of boundary friction and they will reach the bottom of the incline simultaneously.
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@Eric Roberts – Ok. Sorry I was confused that viscosity takes place inside the liquid itself and doesn't depend on friction. I have edited the question.
The answer is incorrect. The viscosity of water is actually larger than the viscosity of the gasoline.
Dynamic viscosity:
water at 20C:1.002x10-3 Ns/m2 or 1.002 centi Poise; gasoline: 0.6 centiPoise
Kinematic viscosity water 1.004 x 10-6 m2/s; gasoline 7.1 x 10-7 m2/s
More importantly the Reynolds number for the flow will be in all likelihood so large that the viscosity does not matter at all . There is a large body of literature, mostly at graduate level, that discusses the crossover from laminar flow (when the viscosity is important) to turbulent flow (when the viscosity is irrelevant).
The correct answer is that the two container will empty in about the same time.
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These containers would be considered "smooth" in any real world application. For smooth conduit, even for very large Reynolds numbers, viscosity is still relevant. Unless you feel that they would be higher than 1 0 8 ?
See: https://en.wikipedia.org/wiki/Moody_chart
Other than that I agree, He shouldn't have picked viscosities so close together that they may actually be transposed.
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Interesting point. The Moody chart you quoted is used for long pipes, where the surface irregularities create the turbulence. Here it is more likely that turbulence is created when the water flow is narrowed by the outlet valve, which has an inside size (diameter and length) of a few centimeter.
My estimation for the Reynolds number, based on the size of the valve (2cm), velocity of water (5m/s) and kinematic viscosity of water (1 X 10^-6 m^2/s) is R=100,000. At this Reynolds number the flow around a sphere (that is a very well studied system) is well in the turbulent regime. I am sure the flow across a valve has been also studied. In a quick search I found this article https://history.nasa.gov/SP-367/f31.htm , where they say that the flow is laminar for R<2,100 and fully turbulent flow sets in for R>40,000
The water would empty first because both would have something between residue and a puddle remaining based on the illustration. The remaining water would evaporate before the mustard oil.
Simple explanation, water is thinner than oil, thus will flow smoother and faster than oil.
I am so confused😑
Guys, discharge=velocity*area, Velocity=√2gh H=height, Viscosity doesn't shows up in this equation, As per this ,they should empty together. Can anybody help?
In a certain amount of time the volume of water and petrol discharged is not the same so you cannot say that there velocity will be same.
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Ram it is correct that they both will empty together as the velocity of efflux in both cases does not depends on the fluid . You may refer to the Torricelli's theorem
Yes, that is correct. I just guessed :(
this why the viscosity index was brought about as there are differences in the flow of liquids. so you would say treacle would flow the same as water?
actually discharge is vel* area for common liquid but for different liquids, it is density vel area
There is friction with the inside wall of the tank. This scales with viscosity index. Thus viscosity ia relevant.
Velocity is influenced by friction & friction will be more in the fluid which has more viscosity.
According to Wikipedia (https://en.wikipedia.org/wiki/Discharge (hydrology)#Theory and_calculation), discharge only applies to the flow of water.
In other way if you pressure at bottom =density g h,,,,so for water pressure difference between container and atm is more so,,,flow is more faster in case of water
The evaporation rate of petrol is to be taken into consideration Petrol has a lover viscosity rating
You have to use your intuition to solve this problem.
I'm confused. Why are people talking about petrol?
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The initial question was on petrol but the staff later changed it to mustard oil.
I think that the outlet is above the bottom most point of the tank, therefore both the tanks can't be emptied.
Just imagine you change the mustard oil to "glue", then the answer is obvious...
But I think glue will be more viscous than petrol.
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Yeah, but both of them are more viscous than water.
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Yes. But petrol will be more appropriate as the viscosity of petrol (= 0.0002) is somewhat near to that of water (= 0.0001). So that the solver will think before he answers this question.
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@Ram Mohith – Only if one's stuck with numbers to judge their lives
where's all the petrol coming from were only talking water and mustard oil. why do people always try to complicate things?
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The question was changed recently (yesterday itself) but this solution was posted on Nov 20.
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I've editted the solution. BTW, why would you change the problem to mustard oil?
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@X X – Because the viscosity of petrol is less than water petrol will get emptied first.
The refractive index of mustard oil is higher than that of water. Thus, mustard oil is optically denser than water. The rate of flow of a liquid is inversely proportional to it's density. So water, with a lower density, will flow faster than mustard oil.
Imagine mercury in one tank that would be interesting.
Pressure = (Density) x (acc. due to gravity) x (Height)
Since they are identical tanks and are in same value of 'g'
the pressure of the flow depends only on density
=> [ Water is more denser the mustard oil ]
[ so the pressure of flow is greater in water than in oil ]
Hence it empties first ;-)
My answer is that water is more dense than oil. Since they are both filled with the same amount then the water will be under more pressure, so it will flow out faster and empty first.
This is false. Water is indeed more dense than oil and its hydrostatic pressure will be more. But since it's denser, it requires a larger pressure for the same efflux rate. In reality, these both cancel out and the rate of efflux is dependent only on the height of the orifice. For more information, check out Torricelli's theorem.
It is not only because of the viscosity, but also because the water is denser than oil, so the pressure at the bottom of the water tank is higher than the pressure at the bottom of the oil tank
How would temperature play a difference? Oil becomes less viscous as temperature climbs
Blood is thicker than water. In this case mustard oil is.
viscosity is the resistance to flow right. It turns out if you're the cook of your family, you'll notice that oil flows slowly compared to liquid water. Thus, if oil flows slowly, then it must have a hard time getting itself to be empty, on the other hand, water flows faster than oil so the ram with liquid water will be empty first
DUDE ITS MORE SIMPLE THAN YOU THOUGH. THE WATER IS LIGHTER AND LESS DENSE THAN OIL SO, IT IS OBVIOUS THAT IT WILL FLOW WAY FASTER THAN IT.
So oil is heavier and denser than the water it floats on?
False conclusion. A denser fluid also requires a greater pressure to have the same mass flow rate.
Viscosity of oil prevents it from friction free flow, therefore, it will take more time to empty as compared with water.
I'm also stumped. If viscosity or density is not the deciding factor then what is? If it has something to do with the coefficient of discharge then please tell.
Water is like water, petrol is like petrol. Unless the petrol undergoes certain frequencies unfamiliar with the systems it surrounds, then petrol will be monitored for multi-dimensional and spacial displacements and other effects, but only monitored. Petrol is emptied first.
whats this all about sounds like using long words to confuse.
I'm going haywire.
F=m*a F means net force applied on the flowing liquid and it pulls the liquids towards the ground. Since a (acceleration) is equal and =9,81 because of gravity (the tanks are both on earth and on the same altitude), mass is the determining factor here. m=d.V Since volumes of the liquids are equal, density determines mass which determines F. The greater the density, the greater the mass. The greater the mass, the greater the force pulling the liquid towards the ground. The harder the liquid is pulled towards the ground, the faster it empties. Water is denser and consequently empties faster.
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The answer is the tank filled with water will be emptied first . The reason lies in the fact that water is less viscous than mustard oil so there will be less resistance to the motion of water molecules and hence water gets emptied with more speed and takes less time than mustard oil. The viscosity of water is so low that it is often considered as non-viscous fluid. Mustard oil has more viscosity than water and hence it's molecules experience more resistance than that of water molecules. So, mustard oil takes more time to get emptied than water.