What is Torricelli's law: Definition and 20 Discussions
Torricelli's law, also known as Torricelli's theorem, is a theorem in fluid dynamics relating the speed of fluid flowing from an orifice to the height of fluid above the opening. The law states that the speed v of efflux of a fluid through a sharp-edged hole at the bottom of a tank filled to a depth h is the same as the speed that a body (in this case a drop of water) would acquire in falling freely from a height h, i.e.
v
=
2
g
h
{\displaystyle v={\sqrt {2gh}}}
, where g is the acceleration due to gravity (9.81 m/s2 near the surface of the Earth). This expression comes from equating the kinetic energy gained,
1
2
m
v
2
{\displaystyle {\frac {1}{2}}mv^{2}}
, with the potential energy lost, mgh, and solving for v. The law was discovered (though not in this form) by the Italian scientist Evangelista Torricelli, in 1643. It was later shown to be a particular case of Bernoulli's principle.
We can derive it by using Bernoulli's equation ##p_0+h_0\rho g+\frac12 \rho {v_0}^2=p_1+h_1\rho g+\frac12 \rho {v_1}^2##, where ##v_0=0## is a velocity of a water surface and ##h_0## is its height. ##h_1## is a height of the outlet above the bottom of a tank the water is in. I am confused about...
Here is only my solution:
##A_1 \frac{\mathrm d h}{\mathrm d t}=-A_2\sqrt{2hg}##,
so by integrating we get
##h(t)=\left(\sqrt{h_0}-\frac{A_2}{2A_1}\sqrt{2g} t\right)^2.##
Setting ##h(T)=0## we get
##T=\frac{A_1}{A_2}\sqrt{\frac{2h_0}{g}}.##
By doing the first time derivative of ##h## we...
There is a standard proof of this kind in which two points are taken - one at the top of the water and one just outside the spout or opening. I guess my question kind of assumes that you've seen something like this.
A key step of the proof is to say that the difference of pressures, perhaps...
Hello,
I'm just starting my research on a project I would like to build. But the design on the project has been delayed until I can get a concrete answer to this problem.
I grew up loving the "The Professor" segments on a kids show from the 70's called "The Hilarious House of Frightenstein"...
Hello Forum,
The speed of water exiting from a side narrow hole at depth h in a large bucket is given by ##v=\sqrt{2gh}##.
This result is obtained applying Bernoulli's equation along a streamline that goes from the top free surface to the drain on the side of the bucket at depth h.
The water...
A cone-shaped water tank is given by V(h)=\pi(h-\frac{h^2}{3}+\frac{h^3}{27})
Show using Torricelli's law law that
-2\sqrt2\pi(\frac{1}{\sqrt{h}}-\frac{2}{3}\sqrt h+\frac{1}{9}h^{3/2})\frac{dh}{dt}=1
What I have done so far:
V'=\frac{1}{9}\pi(h-3)^2h'
What I know: Below link is about Torricelli's law. Velocity of liquid coming out of bottom of the tank i.e comes after using Bernoulli's equation square root of (2*g*h*) where "h" is height of fluid in the container and "g" is acceleration due to gravity...
Based on the law of mass continuity, when a pipe narrows then the speed of the fluid increases. Then why is it that when draining a tank the speed of the fluid only depends on the height of water above and not on the size of the hole? Wouldn't a narrower hole mean that that the speed must be...
Homework Statement
(This is a continuation of the problem where I proved Torricelli's Law: v = √(2gh))
The water level in a tank lies a distance H above the floor. There is a hole in the tank that a distance h below the water level
a.) Find the distance x from the wall of the tank at which the...
Homework Statement
An open cylinder of height 5ft and cross sectional area of 1 ft2 is initially empty. There is a small hole at the bottom of the cylinder with an area of 0.005 ft2. Water is drawn into the tank at a rate of 4.8ft3/min. At the same time water is discharged out of the...
Homework Statement
A spherical tank of radius 4(ft) is full of gasoline when a circular bottom hole with radius 1 in. is opened. How long will be required for all the gasoline to drain from the tank?
Homework Equations
dVolume/dTime = -a(2gy)^(1/2)
The Attempt at a Solution
Right...
I am reading through my fluid mechanics book and there is a derivation of Torricelli's theorem i.e. V = \sqrt{2gh}.
The author's pick the datum line at the middle of the jet and show that:
h = \dfrac{p}{\gamma} + \dfrac{V^2}{2g}
where h is the distance from the jet to the surface of the...
Hey I have a question on the derivation of Torricelli's Law. Bernoulli's Equation states the following:
Now let's say that the left side of the equation is the top of the tank and the right side of the equation is the bottom of the tank. The origin is at the bottom of the tank.
We can...
HELP! Diff Eqs, Torricelli's law
Hi, my crazy diff eq professor for some reason decided to assign us a project accompanied by some book problems right in the middle of exam week, due friday (day of my last exam). This is easily the most redic. thing I've ever seen in my college career. Anyhow...
Homework Statement
Sprinkler in a hotel is supplied by gravity from a cylindrical tank on the roof. Suppose the tank has a radius of 25' and the diameter of the outlet is 4". The system must provide 2270 psf for at least 5 minutes. What height should the engineer specify for the tank to...
Homework Statement
If a tank holds 5,000 gallons of water which drains from the bottom of the tank
in 40 minutes, then Torricelli's Law gives the volume V of water reminaing in the
tank after t minutes as
V = 5000(1 - t / 40)2, 0 <= t <= 40. The rate at which water is
draining from...
Homework Statement
ok, I am doing an assignment on torricellis law but I have run into a big problem. I have a bowl which can be described by the function:
squareroot(1/0.11*h). This bowl has a hole in the bottom of a radius of 0.004m. But when I use the relavant formula and integrate it...
Homework Statement
I must derive Torricelli's law.
Homework Equations
P+\rho gh +\frac{\rho v^2}{2} = \text{constant}.
The Attempt at a Solution
I chose the origin of the system as being on the surface of the liquid.
I have that P_0 = P_1+ \frac{\rho v_1^2}{2}.
But P_1=P_0+\rho...
I would be grateful for any assistance with the following Torricelli's law problem :yuck:
Homework Statement
I have a cylindrical tank that is oriented horizontally, with an end radius of 3 feet and a length of 5 feet. (It's a math text, so no SI units for me.) The tank is half-full of...
Hey there.
I'm currently taking grade 11 physics, and as part of our final evaluation, we have to perform an in-class lab. We're not given the procedure, just what we have to determine and a list of apparatus. I have a general idea of what to do, but I'd just like some confirmation if what I'm...