Answer
414.6k+ views
Hint:-
The reason behind the lifting of the roof is Bernoulli’s principle. According to the principle, the pressure on one side of the surface is equal to the other side of the surface. Here, at the top of the roof there is low pressure as the wind is blowing while below the roof there is high pressure as there is no wind flowing inside the house. So, the high pressure in the inside and low pressure on the outside of the roof causes the roof to lift up.
Complete step-by-step solution
${p_1} + \rho gh + \dfrac{1}{2}{\rho _1}v_1^2 = {p_2} + \rho gh + \dfrac{1}{2}{\rho _2}v_2^2$;
Cancel out the common variables, put ${v_1} = v$and${v_2} = 0$;
${p_2} = {p_1} + \dfrac{1}{2}{\rho _1}v_1^2$;
\[{p_2} - {p_1} = \dfrac{1}{2}{\rho _1}v_1^2\];
Here: $\Delta p = {p_2} - {p_1}$;
$\Delta p = \dfrac{1}{2}{\rho _1}v_1^2$;
Put${v_1}$= v in the above equation:
$\Delta p = \dfrac{1}{2}\rho {v^2}$;
${p_2} - {p_1} = \dfrac{1}{2}\rho {v^2}$;
Apply the relation between force and pressure:
$({P_1} - {P_2}) = \dfrac{F}{A}$;
$F = ({P_1} - {P_2}) \times A$;
Put the value ${p_2} - {p_1} = \dfrac{1}{2}\rho {v^2}$in the above equation:
$F = \dfrac{1}{2}\rho {v^2} \times A$;
Here $v = 108km{h^{ - 1}}$is equal to$v = \dfrac{{108 \times 1000}}{{60 \times 60}} = 30m/s$;
\[F = \dfrac{1}{2} \times 1.3 \times 900 \times 40\];
Do the necessary calculation:
\[F = \dfrac{{46800}}{2}\];
The lift force is given as:
\[F = 23,400N\];
\[F = 2.34 \times {10^4}N\];
Final Answer: Option”3” is correct. The magnitude of aerodynamic lift on the roof is\[2.34 \times {10^4}N\].
Note:- Here we have to find the difference in pressure by applying Bernoulli’s theorem and then apply the formula$F = ({P_1} - {P_2}) \times A$. After applying Bernoulli’s equation the common terms $\rho gh$will cancel out and the final velocity ${v_2}$will be zero. In the end we will get the force which is also known as lift force and is equal to the magnitude of aerodynamic lift on the roof.
The reason behind the lifting of the roof is Bernoulli’s principle. According to the principle, the pressure on one side of the surface is equal to the other side of the surface. Here, at the top of the roof there is low pressure as the wind is blowing while below the roof there is high pressure as there is no wind flowing inside the house. So, the high pressure in the inside and low pressure on the outside of the roof causes the roof to lift up.
Complete step-by-step solution
${p_1} + \rho gh + \dfrac{1}{2}{\rho _1}v_1^2 = {p_2} + \rho gh + \dfrac{1}{2}{\rho _2}v_2^2$;
Cancel out the common variables, put ${v_1} = v$and${v_2} = 0$;
${p_2} = {p_1} + \dfrac{1}{2}{\rho _1}v_1^2$;
\[{p_2} - {p_1} = \dfrac{1}{2}{\rho _1}v_1^2\];
Here: $\Delta p = {p_2} - {p_1}$;
$\Delta p = \dfrac{1}{2}{\rho _1}v_1^2$;
Put${v_1}$= v in the above equation:
$\Delta p = \dfrac{1}{2}\rho {v^2}$;
${p_2} - {p_1} = \dfrac{1}{2}\rho {v^2}$;
Apply the relation between force and pressure:
$({P_1} - {P_2}) = \dfrac{F}{A}$;
$F = ({P_1} - {P_2}) \times A$;
Put the value ${p_2} - {p_1} = \dfrac{1}{2}\rho {v^2}$in the above equation:
$F = \dfrac{1}{2}\rho {v^2} \times A$;
Here $v = 108km{h^{ - 1}}$is equal to$v = \dfrac{{108 \times 1000}}{{60 \times 60}} = 30m/s$;
\[F = \dfrac{1}{2} \times 1.3 \times 900 \times 40\];
Do the necessary calculation:
\[F = \dfrac{{46800}}{2}\];
The lift force is given as:
\[F = 23,400N\];
\[F = 2.34 \times {10^4}N\];
Final Answer: Option”3” is correct. The magnitude of aerodynamic lift on the roof is\[2.34 \times {10^4}N\].
Note:- Here we have to find the difference in pressure by applying Bernoulli’s theorem and then apply the formula$F = ({P_1} - {P_2}) \times A$. After applying Bernoulli’s equation the common terms $\rho gh$will cancel out and the final velocity ${v_2}$will be zero. In the end we will get the force which is also known as lift force and is equal to the magnitude of aerodynamic lift on the roof.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)