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
How many moles of nitrogen trifluoride (NF3) can be produced from 9.65 mole of Fluorine gas (F2)
user100 [1]

Answer:

6.43 moles of NF₃.

Explanation:

The balanced equation for the reaction is given below:

N₂ + 3F₂ —> 2NF₃

From the balanced equation above,

3 moles of F₂ reacted to produce 2 moles of NF₃.

Finally, we shall determine the number of mole of nitrogen trifluoride (NF₃) produced by the reaction of 9.65 moles of Fluorine gas (F₂). This can be obtained as follow:

From the balanced equation above,

3 moles of F₂ reacted to produce 2 moles of NF₃.

Therefore, 9.65 moles of F₂ will react to to produce = (9.65 × 2)/3 = 6.43 moles of NF₃.

Thus, 6.43 moles of NF₃ were obtained from the reaction.

4 0
3 years ago
Which of the following statements is incorrect? A. Molecular mass is expressed in atomic mass units. B. Formula mass compares th
n200080 [17]

Answer:

  • The incorrect statement is the choice <em>C. Atomic mass has units of grams per atom.</em>

Explanation:

<u>1) Choice A.</u><em><u> Molecular mass is expressed in atomic mass units</u></em><u>.</u>

Correct. Atomic mass units (a.m.u) is the standard unit used to express the mass of the atoms and the molecules.

Since, one atom, molecule, or formula unit is a tiny amount of material, it has a ver, very low mass, and the unit mass of a molecule is referred to one mole (6.022 × 10²³ units).

<u>2) Choice B. </u><em><u>Formula mass compares the mass of one formula unit of a substance to the mass of one atom of carbon-12</u></em><u>.</u>

Correct. The masses of atoms and compounds are referred to a standard. Such standard is the carbon-12 atom. This is, the cabon-12 atom was selected as the standard and its exact mass is 12 a.m.u.

<u>3)  Choice C. </u><em><u>Atomic mass has units of grams per atom.</u></em><u> </u>

Incorrect. Atomic mass is the mass of the atoms, but, since, the mass of one atom is so small, the atomic mass is referred to one mole. Hence, the atomic mass has units of grams per mole.

<u>4) Choice D. </u><em><u>Both molecular mass and formula mass use carbon-12 as a reference standard.</u></em>

Correct. As stated when explaining the option B, the mass of atoms, molecules, and formula units are referred to carbon-12 standard.

<u>5) Choice E. S</u><em><u>odium chloride, an ionic compound, is said to have a formula weight, but not a molecular weight.</u></em>

Correct. The reason is that ionic compounds form large structures (crystals) and, since there is not such thing as one molecule of them, they are said to have formula weight (or mass) but not a molecular weight.

The name molecules is reserved for covalent compounds, where you can formally identify molecules. E.g. Water is a molecular compound, and each molecule has molecular formula H₂O, whose mass is the molecular mass.

7 0
3 years ago
Which of the following statements is true?
Lostsunrise [7]
<span>2. Light energy does not require a medium through which to travel.

Hope this helps!</span>
5 0
3 years ago
Read 2 more answers
1 Identify Draw an example of a force acting on an object.
Alisiya [41]

Answer:

Answer below

Explanation:

Just draw a photo of someone pushing an object across a table. Your push is the force acting on the object you're pushing.

5 0
2 years ago
The chemical properties of calcium are most similar to the chemical properties of
Ket [755]
The answer is (3) Mg because Ca and Mg are in the same group (group 2). 
Hope this helps~
3 0
3 years ago
Other questions:
  • On combustion, 1.0 L of a gaseous compound of hydrogen, carbon, and sulfur gives 2.0 L of CO2, 3.0 L of H2O vapor, and 1.0 L of
    15·1 answer
  • Dalton’s atomic theory included which idea?
    14·1 answer
  • When chlorine gas is passed through a potassium bromide solution, bromine forms in a potassium chloride solution?
    9·1 answer
  • A force of 24 N acts on an 8 kg rock. What is the acceleration of the rock?
    14·1 answer
  • What is the mass of 0.46 mol of MgCl2
    5·1 answer
  • HURRY PLS IT'S TIMED
    14·2 answers
  • Hey, it'd be really cool if someone could help me with this-- 15 pts!
    5·1 answer
  • How do you detect which material is going to be positively charged or negatively charged?
    13·1 answer
  • Please help me with this science ​
    10·1 answer
  • What will happen to the pH of sodium bicarbonate if vinegar is added to it?​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!