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
Otrada [13]
3 years ago
15

An air stream enters a variable area channel at a velocity of 30 m/s with a pressure of 120 kPa and a temperature of 10°C. At a

certain point in the channel, the velocity is found to be 250 m/s. Using Bernoulli’s equation (i.e., p + rhoV2 /2 = constant), which assumes incompressible flow, find the pressure at this point. In this calculation, use the density evaluated at the inlet conditions. If the temperature of the air is assumed to remain constant, evaluate the air density at the point in the flow where the velocity is 250 m/s. Compare this density with the density at the inlet to the channel. Based on this comparison, do you think that the use of Bernoulli’s equation is justified
Chemistry
1 answer:
nekit [7.7K]3 years ago
8 0

Answer:

P₂= 74 kPa under constant density and ρ₂ = 1.06 kg/m³ (-38.6% of error compared with incompresible assumption) . Thus Bernoulli’s equation should not be applied

Explanation:

Assuming ideal gas behaviour of air , then

P*V= n*R*T = m / M * R *T

since

ρ= m/V = P*M /( R *T)

where

n= moles , V= volume , m= mass

ρ= density

P= pressure = 120 kPa= 120000 Pa

M= molecular weight of air = 0.21*32+0.79*28= 28.24 gr/mol = 0.02824 kg/mol

T= absolute temperature = 10°C + 273 = 283 K

R= ideal gas constant = 8.314 J/mol K

solving for ρ

ρ=  P*M /( R *T) = 120000 Pa*0.02824 kg/mol/(8.314 J/mol K*283 K) = 1.47 kg/m³

then from Bernoulli's equation

P₁ + ρ*v₁²/2 = P₂ + ρ*v₂²/2

where 1 denotes inlet and 2 denotes other point , p = pressure and v= velocity . Then solving for p₂

P₁ + ρ*v₁²/2 = P₂ +ρ*P₂²/2

P₂=  P₁ +ρ*v₁²/2 - ρ*v₂²/2  = P₁ +ρ/2*(v₁² - v₂²)

replacing values

P₂= P₁ +ρ/2*(v₁² - v₂²) = 120000 Pa + 1.47 kg/m³/2*[(30 m/s)²-(250 m/s)²] = 74724 Pa = 74 kPa

P₂= 74 kPa

then if the temperature remains constant

ρ₁= P₁*M /( R *T) and ρ₂= P₂*M /( R *T)

dividing both equations

ρ₂/ρ₁ = P₂/ P₁

ρ₂ = (P₂/ P₁)*ρ₁

then from Bernoulli's equation

P₁ + ρ₁*v₁²/2 = P₂ + ρ₂*v₂²/2

P₂ = P₁ + ρ₁*v₁²/2 - ρ₂*v₂²/2

therefore

ρ₂ = (P₂/ P₁)*ρ₁ = (P₁ + ρ₁*v₁²/2 - ρ₂*v₂²/2 ) /P₁ *ρ₁

P₁ * ρ₂  = P₁ *ρ₁  + ρ₁²*v₁²/2 - ρ₂*ρ₁ * v₂²/2

P₁ * ρ₂ + ρ₂*ρ₁ * v₂²/2  = P₁ *ρ₁  + ρ₁²*v₁²/2

ρ₂* (P₁ + ρ₁ * v₂²/2) = P₁ *ρ₁  + ρ₁²*v₁²/2

ρ₂ = (P₁ *ρ₁  + ρ₁²*v₁²/2)/(P₁ + ρ₁ * v₂²/2) =  (P₁ + ρ₁*v₁²/2)/(P₁/ρ₁ + v₂²/2)

replacing values

ρ₂ = ( 120000 Pa + 1.47 kg/m³/2*(30 m/s)²)/(120000 Pa/1.47 kg/m³+1/2*(250 m/s)²)

ρ₂ = 1.06 kg/m³

the error of assuming constant ρ would be

e = (ρ₂ - ρ)/ρ₂=  1- ρ/ρ₂= 1- 1.47 kg/m³/1.06 kg/m³ = -0.386 (-38.6%)

thus Bernoulli’s equation should not be applied

You might be interested in
Which of the atoms below are least likely to violate the octet rule?
Levart [38]

Answer:

F i think i pretty sure F!!!!!!!!

5 0
3 years ago
Consider the reaction of peroxydisulfate ion (S2O2−8) with iodide ion (I−) in aqueous solution: S2O2−8(aq)+3I−(aq)→2SO2−4(aq)+I−
kolbaska11 [484]

Answer:

r = 3.61x10^{-6} M/s

Explanation:

The rate of disappearance (r) is given by the multiplication of the concentrations of the reagents, each one raised of the coefficient of the reaction.

r = k.[S2O2^{-8} ]^{x} x [I^{-} ]^{y}

K is the constant of the reaction, and doesn't depends on the concentrations. First, let's find the coefficients x and y. Let's use the first and the second experiments, and lets divide 1º by 2º :

\frac{r1}{r2} = \frac{0.018^{x} x0.036^{y} }{0.027^xx0.036^y}

\frac{2.6x10^{-6}}{3.9x10^{-6}} = (\frac{0.018}{0.027})^xx(\frac{0.036}{0.036})^y

0.67 = 0.67^x

x = 1

Now, to find the coefficient y let's do the same for the experiments 1 and 3:

\frac{r1}{r3} = \frac{0.018x0.036^y}{0.036x0.054^y}

\frac{2.6x10^{-6}}{7.8x10^{-6}} = (\frac{0.018}{0.036})x(\frac{0.036}{0.054})^y

0.33 = 0.5x 0.67^y

0.67 = 0.67^y

y = 1

Now, we need to calculate the constant k in whatever experiment. Using the first :

2.6x10^{-6} = kx0.018x0.036kx6.48x10^{-4} = 2.6x10^{-6}

k = 4.01x10^{-3} M^{-1}s^{-1}[/tex]

Using the data given,

r = 4.01x10^{-3}x1.8x10^{-2}x5.0x10^{-2}

r = 3.61x10^{-6} M/s

7 0
3 years ago
How many liters in 4.4 grams of CO2 at STP?
d1i1m1o1n [39]

Answer:

2.24 Liters are in 4.4 grams of CO2 at STP

5 0
4 years ago
If an atom has an atomic mass of 16 and it has 8 neutrons what is it's atomic number
Lana71 [14]
The atomic number is 8.
7 0
3 years ago
Which is nitrated faster toluene or nitrobenzoate and why<br>​
Nataly_w [17]
The Malcontents' major complaints were that the Trustees had placed too many limitations on the ownership of land, the right to make and to buy alcohol, and the right to own slaves.
4 0
3 years ago
Other questions:
  • Properties of group 7 (aka. The Halogens)?
    6·1 answer
  • Which products would form if chlorine gas was bubbled through a solution of sodium bromide?
    6·1 answer
  • Which of the following types of energy equals the total energy of motion and position
    9·1 answer
  • Which example best represents the use of creativity in scientific inquiry?
    7·2 answers
  • A flexible container at an initial volume of 3.10 L contains 9.51 mol of gas. More gas is then added to the container until it r
    10·1 answer
  • What is the resistance of a blub when the voltage across is 6 V and the current is 0.2A?
    14·1 answer
  • How much energy is released when 2.25kg of water cools from 99.5°C to 4.2°C? 1000g=1kg; 1000J=1kJ; specific heat of water 4.184J
    7·1 answer
  • How can we use properties to identify unknown minerals?
    9·2 answers
  • Compounds containing potassium and oxygen
    15·1 answer
  • The barium ion Ba2+ combines with the phosphate ion PO43- to form an ionic compound. Which is the formula for that compound?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!