1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
raketka [301]
3 years ago
10

Water (with density of 1000 kg/m3) with the mass flowrate of 10 kg/sec is flowing into an empty tank. The outlet volumetric flow

rate (m3/sec) from the tank is 0.01 times of the liquid height (in meter) in the tank. If the cross section area of thank is 0.01 m2 how long does it take to fill the tank up to 0.6 meter from the bottom? how long does it take to fill the tank up to 2 meter from the bottom?
Chemistry
1 answer:
Montano1993 [528]3 years ago
8 0

Explanation:

Apply the mass of balance as follows.

   Rate of accumulation of water within the tank = rate of mass of water entering the tank - rate of mass of water releasing from the tank

         \frac{d}{dt}(\rho V) = 10 - \rho \times (0.01 h)

      \rho A_{c} \frac{dh}{dt} = 10 - (0.01) \rho h

   \frac{dh}{dt} + \frac{0.01 \rho h}{\rho A_{c}} = \frac{10}{\rho A_{c}}

          [/tex]\frac{dh}{dt} + \frac{0.01}{0.01}h[/tex] = \frac{10}{\rho A_{c}}

                       A_{c} = 0.01 m^{2}

              \frac{dh}{dt} + h = 1

                  \frac{dh}{dt} = 1 - h

               \frac{dh}{1 - h} = dt  

                \frac{ln(1 - h)}{-1} = t + C      

Given at t = 0 and V = 0  

                         A \times h = 0  

 or,                     h = 0

                 -ln(1 - h) = t + C

Initial condition is -ln(1) = 0 + C

                                C = 0  

                So,   -ln(1 - h) = t

or,                      t = ln (\frac{1}{1 - h})  ........... (1)

(a)    Using equation (1) calculate time to fill the tank up to 0.6 meter from the bottom as follows.

                    t = ln (\frac{1}{1 - h})  

                     t = ln (\frac{1}{1 - 0.6})  

                        = ln (\frac{1}{0.4})

                        = 0.916 seconds

(b)   As maximum height of water level in the tank is achieved at steady state that is, t = \infty.  

                    1 - h = exp (-t)

                    1 - h = 0  

                         h = 1

Hence, we can conclude that the tank cannot be filled up to 2 meters as maximum height achieved is 1 meter.

                 

You might be interested in
What is responsible for the blue sky?​​
andreev551 [17]

Answer:

well for me it's

Explanation:

The reflection of the seas

7 0
3 years ago
Read 2 more answers
The Doppler effect related change in wave frequency to what?
Irina18 [472]

Answer:

Relative motion of source and observer.

Explanation:

Doppler Effect : It is the change in the observed frequency of the wave due to<em><u> relative motion of the source and object </u></em>.

8 0
3 years ago
URGENT<br> What is the total volume of a lead can if it has a mass of 800g.
Sonja [21]

Answer:

750

Explanation:

5 0
3 years ago
How many moles of O2 are consumed if 20 moles of SO2 are produced
tatiyna

Answer:

25

I hope this helps

5 0
3 years ago
Nuclear fusion in the sun involves hydrogen (H) atoms combining to form helium (He). A student claims that since the atmosphere
Lisa [10]

Nuclear fusion in the sun involves hydrogen (H) atoms combining to form helium (He). A student claims that since the atmosphere contains hydrogen, any fusion reaction on Earth would result in an uncontrolled chain reaction. What is wrong in the student’s reasoning is that the uncontrolled chain reactions can only happen during nuclear fission.

5 0
3 years ago
Read 2 more answers
Other questions:
  • 3. What is the relationship between the kinetic energy of gas particles and the
    13·1 answer
  • All of the halogens __________. a. exhibit metallic character b. form salts with alkali metals with the formula mx c. exist unde
    15·1 answer
  • In reversible reaction when do forward reactions take place
    9·1 answer
  • A pet owner dropped some new fish into a pond. Several species of fish lived in the pond, but within a few months, only members
    12·1 answer
  • Which of these molecules has an overall dipole moment? O A. F2 B. H2S C. CH4 D. CO2​
    9·1 answer
  • From the balanced reaction:
    5·1 answer
  • Which of the following is an example of a solution?
    8·1 answer
  • How many grams are in 2.4 moles of calcium chloride
    6·1 answer
  • 7. If you constructed graphs, what trends do they indicate in your data?
    12·1 answer
  • How can u tell if an object has elastic properties
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!