Since the vessel is hemispherical, its volume can be given by:
V=((4/3)(pi)r3)/2
V=(2/3)(pi)r3
where r is the radius of the vessel.
Since water is flowing into the vessel at a constant rate of 1 L/s, the volume of water in the vessel is thereby increasing at a constant rate of 1 L/s.
By deriving the volume equation for the vessel with respect to time, we can equate the rate of change of the volume of water to the rate of change of the radius of the surface of water:
dV/dt = (2/3)(pi)(3r2)(dr/dt)
You must derive implicitly, so r3 derives down to 3r2(dr/dt) since the radius is also in itself a function of time. This equation can be cleaned up:
dV/dt = 2(pi)r2(dr/dt)
By solving for dr/dt, we get an expression for rate of change of the radius of the surface of water.
dr/dt = (dV/dt)/(2(pi)r2)
From the problem, we know that dV/dt is 1 L/s, and the radius of the hemisphere is a constant 0.5 m. We can substitute these known values into the equation:
dr/dt = 1/(2(pi)(0.5)2)
dr/dt = 2/pi
This is the rate of change of the radius of the surface of water. The rate of change is a constant, which is important. Since it is constant, you can simply multiply this rate of change by a quantity of time to find the radius of the water level at any specific time. This is analogous to multiplying a constant velocity times a quantity of time to know an object's position at that time (a rate of change times an amount of change). We know that the vessel has an overall radius of 0.5 m, so the radius of the surface of water cannot exceed 0.5m.
(dr/dt)= 2/pi
therefore, depth at time t, D= 2t/pi
This model gives the depth of the water (D) at any given time (t). As t increases, D(t) will return larger and larger values, which is expected since the water depth will increase as more water flows in.
Yes, if the process is occurring under an isothermal condition where change in T=0
A ten-sided polygon is called a decagon. A decagon has ten internal angles of 144-degrees. All sides of a regular decagon are equal length.
It means a situation is becoming exciting or dangerous. Placing a piece of fat in fire will cause it to cook so quickly parts of it will turn into boiling liquid, melt through the internal structures and explode into the air. This is very hot bits of oil that can burn a person on contact.
Gross Heat Rate: Gross electricity (Power) produced by a power plant per unit fuel energy consumption. This excludes all internal power consumptions. Net Heat rate is net power production at transformer per unit fuel energy consumption by power plant.
72(t) Calculator: Early withdrawals from retirement accounts The Internal Revenue Code section 72(t) and 72(q) allows for penalty free early withdrawals from retirement accounts. These sections allow you to begin receiving money from your retirement accounts before you turn age 59-1/2 without the normal 10% premature distribution penalty. Use this calculator to determine your allowable 72(t)/(q) Distribution and how it can help fund your early retirement. The IRS rules regarding 72(t)/(q) Distributions are complex. Please consult a qualified professional when making decisions about your personal finances. Please note that your financial institution may or may not support all the methods displayed via this calculator.
Crystal shape is the outward expression of the internal arrangement of atoms, held together in a specific geometrical arrangement.
Crystal shape is the outward expression of the internal arrangement of atoms, held together in a specific geometrical arrangement.
It is called homeostasis (internal environment maintained at a constant level) or thermostasis (internal heat maintained at a constant temperature). The overall name for the processes by which temperature is controlled is thermoregulation.
Homeostasis is the regulation of internal biochemistry to maintain a constant internal environment. Without this constant regulation, living organisms would be unable to function. Therefore, homeostasis is the regulation of the internal environment of the body, and also the maintenance of this constant environment. Hope this helps!
Homeostasis is the regulation of internal biochemistry to maintain a constant internal environment. Without this constant regulation, living organisms would be unable to function. Therefore, homeostasis is the regulation of the internal environment of the body, and also the maintenance of this constant environment. Hope this helps!
homeostasis
The internal resistance of a cell is not constant because a cell needs to move and be flexible in order to undergo various osmosis or diffusion processes.
A hemi engine refers to one of the most popular high performance engine types.
The maintenance of a constant internal state in a changing movement.
facial expression matched their internal feelings.
yes
Hemostasis means control of bleedingit is constant internal chemical composition