Water or Mustard oil?

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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The tank filled with mustard oil The tank filled with water

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14 solutions

Ram Mohith
Nov 20, 2018

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 \color{#3D99F6}\textbf{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.

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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

Ram Mohith - 2 years, 6 months ago

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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

Jeremy Galvagni - 2 years, 6 months ago

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@Jeremy Galvagni I have seen it in a problem that viscosity of petrol is 0.002

Ram Mohith - 2 years, 6 months ago

how about petrol is less density than water?

Ahmed Almubarak - 2 years, 6 months ago

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The density doesn't matter: as for a stone, the heaviest doesn't fall faster.

Bastien Faller - 2 years, 6 months ago

Are you sure that water is less viscous than petrol? Where did you find these values?

Bastien Faller - 2 years, 6 months ago

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Yes. I am sure about it.

Ram Mohith - 2 years, 6 months ago

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.

Eric Roberts - 2 years, 6 months ago

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I edited the question afterwards thinking that the answer will be correct only if friction is absent.

Ram Mohith - 2 years, 6 months ago

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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.

Eric Roberts - 2 years, 6 months ago

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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.

Ram Mohith - 2 years, 6 months ago

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.

Laszlo Mihaly - 2 years, 6 months ago

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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 10^8 ?

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.

Eric Roberts - 2 years, 6 months ago

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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

Laszlo Mihaly - 2 years, 6 months ago

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.

Alan Burke - 2 years, 5 months ago

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This is my favorite explanation.

Ryan Reichlin - 1 year, 6 months ago

Simple explanation, water is thinner than oil, thus will flow smoother and faster than oil.

Cadillac Jerm - 1 year, 3 months ago

I am so confused😑

Erin Smith - 1 year, 2 months ago
Mak Czar
Nov 21, 2018

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.

Ram Mohith - 2 years, 6 months ago

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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

Rishi dey chowdhury - 2 years, 4 months ago

Yes, that is correct. I just guessed :(

ZANE NABHAN - 2 years, 6 months ago

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?

Christopher Joyson - 2 years, 6 months ago

actually discharge is vel* area for common liquid but for different liquids, it is density vel area

Mohammad Shahid - 2 years, 6 months ago

There is friction with the inside wall of the tank. This scales with viscosity index. Thus viscosity ia relevant.

Manuel Chaniotakis - 2 years, 6 months ago

Velocity is influenced by friction & friction will be more in the fluid which has more viscosity.

Anupam Deep - 2 years, 5 months ago

According to Wikipedia (https://en.wikipedia.org/wiki/Discharge (hydrology)#Theory and_calculation), discharge only applies to the flow of water.

Toby M - 2 years, 5 months ago

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

Dharambir Poddar - 2 years, 5 months ago

The evaporation rate of petrol is to be taken into consideration Petrol has a lover viscosity rating

Derek Cook - 1 year, 5 months ago

You have to use your intuition to solve this problem.

Lâm Lê - 1 year, 1 month ago

I'm confused. Why are people talking about petrol?

Saj Tyk - 1 year ago

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The initial question was on petrol but the staff later changed it to mustard oil.

Ram Mohith - 1 year ago
Shreyash Gupta
Jan 11, 2019

I think that the outlet is above the bottom most point of the tank, therefore both the tanks can't be emptied.

X X
Nov 20, 2018

Just imagine you change the mustard oil to "glue", then the answer is obvious...

But I think glue will be more viscous than petrol.

Ram Mohith - 2 years, 6 months ago

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Yeah, but both of them are more viscous than water.

X X - 2 years, 6 months ago

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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.

Ram Mohith - 2 years, 6 months ago

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@Ram Mohith Only if one's stuck with numbers to judge their lives

Akshay Krishna - 2 years, 5 months ago

where's all the petrol coming from were only talking water and mustard oil. why do people always try to complicate things?

Christopher Joyson - 2 years, 6 months ago

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The question was changed recently (yesterday itself) but this solution was posted on Nov 20.

Ram Mohith - 2 years, 6 months ago

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I've editted the solution. BTW, why would you change the problem to mustard oil?

X X - 2 years, 6 months ago

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@X X Because the viscosity of petrol is less than water petrol will get emptied first.

Ram Mohith - 2 years, 6 months ago

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.

Alpha Centauri - 1 year, 7 months ago

Imagine mercury in one tank that would be interesting.

Pat Butler - 1 year, 4 months ago
Goku Hp
Nov 23, 2019

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 ;-)

Carter Jackson
Dec 18, 2018

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.

Anindya Mahajan - 1 year ago
Paul Romero
Mar 22, 2021

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

David Harsant
Feb 6, 2021

How would temperature play a difference? Oil becomes less viscous as temperature climbs

Saj Tyk
May 19, 2020

Blood is thicker than water. In this case mustard oil is.

Arthon Godito
Jan 9, 2020

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

Utsav Playz
Dec 29, 2018

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?

Chris Arsenault - 1 year, 2 months ago

False conclusion. A denser fluid also requires a greater pressure to have the same mass flow rate.

Anindya Mahajan - 1 year ago
Vinod Kumar
Dec 29, 2018

Viscosity of oil prevents it from friction free flow, therefore, it will take more time to empty as compared with water.

Aishwary Omkar
Dec 28, 2018

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.

Scott Ritze
Nov 26, 2018

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.

Christopher Joyson - 2 years, 6 months ago

I'm going haywire.

Akshay Krishna - 2 years, 5 months ago

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.

Güneş Bodur - 1 year, 4 months ago

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