Past paper question about rates

  • Thread starter Thread starter captainjack2000
  • Start date Start date
  • Tags Tags
    Paper
AI Thread Summary
The discussion revolves around calculating the velocity of water exiting a tank and determining the tank's steady-state fullness. Given that water enters the tank at a rate of 0.2 m³/s and exits through a hole with an area of 0.05 m², the relationship between flow rate, velocity, and area is crucial. Participants emphasize using dimensional analysis to equate the inflow and outflow rates, leading to the equation v * 0.05 = 0.2, where v represents the exit velocity. The uncertainty about whether the inflow and outflow rates are equal in steady state is also addressed. Ultimately, understanding these principles is key to solving the problem effectively.
captainjack2000
Messages
96
Reaction score
0

Homework Statement


Water is falling gently into a large tank at 0.2m^3s^-1 and leaves through a small hole in the bottom of the tank of area 0.05m^2. What is the water velocity as it leaves? How full is the tank in the steady state?




Homework Equations


Well if the rate of water entering is 0.2m^3s^-1 by dimensional analysis rate=velocity*area
So the rate of water leaving the tank will be v*Area = v*0.05

I'm not sure how to find the velocity of the water as it leaves the tank because surely these two rates will not be the same (except in the steady state??)
 
Physics news on Phys.org
captainjack2000 said:

Homework Statement


Water is falling gently into a large tank at 0.2m^3s^-1 and leaves through a small hole in the bottom of the tank of area 0.05m^2. What is the water velocity as it leaves? How full is the tank in the steady state?


Homework Equations


Well if the rate of water entering is 0.2m^3s^-1 by dimensional analysis rate=velocity*area
So the rate of water leaving the tank will be v*Area = v*0.05

I'm not sure how to find the velocity of the water as it leaves the tank because surely these two rates will not be the same (except in the steady state??)
You've almost got it.

What is v * Area? or rather what are the units of v * A?
 
Last edited:
sorry what do you mean
how to do change velocity*area?
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Submarine Buoyancy Differential Equation
Replies
3
Views
3K
Water level rise in a tank, continuous flow in, high exit
Replies
11
Views
3K
How Do You Calculate the Flow Rate from a Rectangular Opening in a Tank?
Replies
1
Views
2K
How do we use Bernoulli's Principle in this situation?
Replies
6
Views
2K
Hypothetical Bernoulli situation with Pascals Law(Efflux torcellis result)
Replies
2
Views
1K
Determining the flow rate for a cooling system
Replies
1
Views
2K
Q: Solve Poiseuille's Law for Volume Flow Rate
Replies
2
Views
1K
How Does Atmospheric Pressure Affect Water Stream Shrinkage?
Replies
3
Views
1K
How Does an Ideal Fluid's Velocity Change When Hitting a Vertical Board?
Replies
17
Views
3K
Fluid mechanics water tank level
Replies
7
Views
4K

Hot Threads

Recent Insights

Back
Top