Practice Questions Solutions.1.1
1
Section 2 • • • • • • • • • • • • •
A or a-Area (𝑚2 ) [𝐿]2 D or d- diameter (𝑚) [𝐿] G- gravitational acceleration (𝑚⁄𝑠 2 ) [𝐿][𝑡]−2 H- convective heat transfer (𝑊/𝑚2 𝐾) [𝑀][𝑡]−3 [𝑇]−1 ∆h- Height difference (𝑚) [𝐿] K or k- Conductive heat transfer (𝑊/𝑚𝐾) [𝑀][𝐿][𝑡]−3 [𝑇]−1 L – Length (𝑚) [𝐿] M - molar mass (𝐾𝑔/𝑚𝑜𝑙) [𝑀][𝑛]−1 [𝑀][𝐿]−1 [𝑡]−2 P or p – Pressure (𝑘𝑃𝑎 ) Q or q – volumetric flow rate (𝑚3 /𝑠) [𝐿]3 [𝑡]−1 R or r – radius (𝑚) [𝐿] T – Temperatures (𝐾) [𝑇] T – time (𝑠) [𝑡]
•
u,v – velocity ( 𝑠 )
• • • • •
𝑚
[𝐿][𝑡]−1
𝑉𝑀 – Molar Volume (𝑚3 /𝑘𝑚𝑜𝑙) [𝐿]3 [𝑛]−1 𝑥, 𝑦 - distance (𝑚) [𝐿] 𝜇 - viscosity (𝑃𝑎 𝑠) [𝑀][𝐿]−1 [𝑡]−1 [𝑀][𝐿]−3 𝜌 – density (𝐾𝑔/𝑚3 ) 𝑊
𝜎 – Stefan Boltzman Constant 5.672𝑥10−8 𝑚2 𝐾4
[𝑀][𝑡]−3 [𝑇]−4
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2
Question 1
[𝐸] = [𝜎𝐴𝑇 4 ] = (𝑀 𝑡 −3 𝑇 −4 )(𝐿2 )(𝑇)4 [𝐸] = [𝑀][𝐿]2 [𝑡]−3 Question 2
𝑎𝐺 : [
𝜌𝑎𝑔 ∆ℎ ∆𝑃 ∆𝑃 𝑀𝐿−1 𝑡 −2 ]=[ ] ⟹ [𝑎𝑔 ] = [ ] [=] = = 𝐿𝑡 −2 𝐿 𝐿 𝜌∆ℎ 𝑀𝐿−3 𝐿 −𝐷 4 ∆𝑃 𝐿4 (𝑀𝐿−1 𝑡 −2 ) [𝑢] = [ ][ ] = 2 = 𝐿𝑡 −1 𝐴𝜇 𝐿 𝐿 (𝑀𝐿−1 𝑡 −1 )𝐿 [𝑎𝑔 ] = [𝐿][𝑡]−2 [𝑢] = [𝐿][𝑡]−1
Question 3
[𝐾] = [
𝑢𝜇𝑥 𝐿𝑡 −1 (𝑀𝐿−1 𝑡 −1 )𝐿 ]= ∆𝑃 𝑀𝐿−1 𝑡 −2 [𝐾] = [𝐿]2
Question 4
𝑃 𝑀𝐿−1 𝑡 −2 [𝑒𝑞𝑛] = [ 2 ] = = 𝑀𝐿−3 𝑡 −2 (𝐿)2 𝑟 𝑘𝑡𝑃 𝐿2 𝑡 [𝜙] = [ ] = =1 (𝑀𝐿−1 𝑡 −1 )(𝑀𝐿−1 𝑡 −2 )−1 (𝐿)2 𝜇𝑐𝑃𝑟 2 [𝜙] = 1 [𝑒𝑞𝑛] = [𝑀][𝐿]−3 [𝑡]−2
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3 Question 5
[
𝜇𝐿𝑄 𝜇𝐿𝑢 ]=[ 2] 4 𝑟 𝑑
(𝑀𝐿−1 𝑡 −1 )(𝐿)(𝐿3 𝑡 −1 ) (𝑀𝐿−1 𝑡 −1 )(𝐿𝑡 −1 ) = (𝐿)4 (𝐿)2 𝑀𝐿−1 𝑡 −2 = 𝑀𝐿−1 𝑡 −2
∴ 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙𝑙𝑦 ℎ𝑜𝑚𝑜𝑔𝑒𝑛𝑜𝑢𝑠 Question 6 [𝑏] = [𝑉𝑀 ] = [𝐿]3 [𝑛]−1 [𝑃] = [
𝑎 ] ⟹ [𝑎] = [𝑃𝑉𝑚2 ] = (𝑀𝐿−1 𝑡 −2 )(𝐿3 𝑛−1 )2 𝑉𝑚2 [𝑎] = [𝑀][𝐿]5 [𝑡]−2 [𝑛]−2
Question 7 [
𝑎 ] = 1 ⟹ [𝑎] = [𝑅𝑇𝑉𝑚] = (𝑀𝐿2 𝑡 −2 𝑛−1 𝑇 −1 )(𝑇)(𝐿3 𝑛−1 ) 𝑅𝑇𝑉𝑚 [𝑎] = [𝑀][𝐿]5 [𝑡]−2 [𝐿𝐻𝑠] = [𝑃𝑉𝑚] = (𝑀𝐿2 𝑡 −2 )(𝐿3 𝑛−1 ) [𝐿𝐻𝑠] = [𝑀][𝐿]2 [𝑡]−2 [𝑛]−1
Question 8 [𝑃] = 𝑀𝐿−1 𝑡 −2 [𝜌𝑔ℎ] = (𝑀𝐿−3 )(𝐿𝑡 −2 )(𝐿) = 𝑀𝐿−1 𝑡 −2 [𝜌𝑢2 ] = (𝑀𝐿−3 )(𝐿𝑡 −1 )2 = 𝑀𝐿−1 𝑡 −2
All equal ∴ eqn is homogenous Question 9 [𝑅] = [
(𝑀𝑛−1 )(𝐿𝑡 −1 )2 𝑀𝑢2 ]= 𝑇 𝑇
[𝑅] = [𝑀][𝑛]−1 [𝐿]2 [𝑡]−2 [𝑇]−1
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Section 2 • • • • • • • • • • • • •
A or a-Area (𝑚2 ) [𝐿]2 D or d- diameter (𝑚) [𝐿] G- gravitational acceleration (𝑚⁄𝑠 2 ) [𝐿][𝑡]−2 H- convective heat transfer (𝑊/𝑚2 𝐾) [𝑀][𝑡]−3 [𝑇]−1 ∆h- Height difference (𝑚) [𝐿] K or k- Conductive heat transfer (𝑊/𝑚𝐾) [𝑀][𝐿][𝑡]−3 [𝑇]−1 L – Length (𝑚) [𝐿] M - molar mass (𝐾𝑔/𝑚𝑜𝑙) [𝑀][𝑛]−1 [𝑀][𝐿]−1 [𝑡]−2 P or p – Pressure (𝑘𝑃𝑎 ) Q or q – volumetric flow rate (𝑚3 /𝑠) [𝐿]3 [𝑡]−1 R or r – radius (𝑚) [𝐿] T – Temperatures (𝐾) [𝑇] T – time (𝑠) [𝑡]
•
u,v – velocity ( 𝑠 )
• • • • •
𝑚
[𝐿][𝑡]−1
𝑉𝑀 – Molar Volume (𝑚3 /𝑘𝑚𝑜𝑙) [𝐿]3 [𝑛]−1 𝑥, 𝑦 - distance (𝑚) [𝐿] 𝜇 - viscosity (𝑃𝑎 𝑠) [𝑀][𝐿]−1 [𝑡]−1 [𝑀][𝐿]−3 𝜌 – density (𝐾𝑔/𝑚3 ) 𝑊
𝜎 – Stefan Boltzman Constant 5.672𝑥10−8 𝑚2 𝐾4
[𝑀][𝑡]−3 [𝑇]−4
© Beat Your Course Inc. All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, or sorted in a data base or retrieval system, without the prior written permission of Beat Your Course Inc.
2
Question 1
[𝐸] = [𝜎𝐴𝑇 4 ] = (𝑀 𝑡 −3 𝑇 −4 )(𝐿2 )(𝑇)4 [𝐸] = [𝑀][𝐿]2 [𝑡]−3 Question 2
𝑎𝐺 : [
𝜌𝑎𝑔 ∆ℎ ∆𝑃 ∆𝑃 𝑀𝐿−1 𝑡 −2 ]=[ ] ⟹ [𝑎𝑔 ] = [ ] [=] = = 𝐿𝑡 −2 𝐿 𝐿 𝜌∆ℎ 𝑀𝐿−3 𝐿 −𝐷 4 ∆𝑃 𝐿4 (𝑀𝐿−1 𝑡 −2 ) [𝑢] = [ ][ ] = 2 = 𝐿𝑡 −1 𝐴𝜇 𝐿 𝐿 (𝑀𝐿−1 𝑡 −1 )𝐿 [𝑎𝑔 ] = [𝐿][𝑡]−2 [𝑢] = [𝐿][𝑡]−1
Question 3
[𝐾] = [
𝑢𝜇𝑥 𝐿𝑡 −1 (𝑀𝐿−1 𝑡 −1 )𝐿 ]= ∆𝑃 𝑀𝐿−1 𝑡 −2 [𝐾] = [𝐿]2
Question 4
𝑃 𝑀𝐿−1 𝑡 −2 [𝑒𝑞𝑛] = [ 2 ] = = 𝑀𝐿−3 𝑡 −2 (𝐿)2 𝑟 𝑘𝑡𝑃 𝐿2 𝑡 [𝜙] = [ ] = =1 (𝑀𝐿−1 𝑡 −1 )(𝑀𝐿−1 𝑡 −2 )−1 (𝐿)2 𝜇𝑐𝑃𝑟 2 [𝜙] = 1 [𝑒𝑞𝑛] = [𝑀][𝐿]−3 [𝑡]−2
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3 Question 5
[
𝜇𝐿𝑄 𝜇𝐿𝑢 ]=[ 2] 4 𝑟 𝑑
(𝑀𝐿−1 𝑡 −1 )(𝐿)(𝐿3 𝑡 −1 ) (𝑀𝐿−1 𝑡 −1 )(𝐿𝑡 −1 ) = (𝐿)4 (𝐿)2 𝑀𝐿−1 𝑡 −2 = 𝑀𝐿−1 𝑡 −2
∴ 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑎𝑙𝑙𝑦 ℎ𝑜𝑚𝑜𝑔𝑒𝑛𝑜𝑢𝑠 Question 6 [𝑏] = [𝑉𝑀 ] = [𝐿]3 [𝑛]−1 [𝑃] = [
𝑎 ] ⟹ [𝑎] = [𝑃𝑉𝑚2 ] = (𝑀𝐿−1 𝑡 −2 )(𝐿3 𝑛−1 )2 𝑉𝑚2 [𝑎] = [𝑀][𝐿]5 [𝑡]−2 [𝑛]−2
Question 7 [
𝑎 ] = 1 ⟹ [𝑎] = [𝑅𝑇𝑉𝑚] = (𝑀𝐿2 𝑡 −2 𝑛−1 𝑇 −1 )(𝑇)(𝐿3 𝑛−1 ) 𝑅𝑇𝑉𝑚 [𝑎] = [𝑀][𝐿]5 [𝑡]−2 [𝐿𝐻𝑠] = [𝑃𝑉𝑚] = (𝑀𝐿2 𝑡 −2 )(𝐿3 𝑛−1 ) [𝐿𝐻𝑠] = [𝑀][𝐿]2 [𝑡]−2 [𝑛]−1
Question 8 [𝑃] = 𝑀𝐿−1 𝑡 −2 [𝜌𝑔ℎ] = (𝑀𝐿−3 )(𝐿𝑡 −2 )(𝐿) = 𝑀𝐿−1 𝑡 −2 [𝜌𝑢2 ] = (𝑀𝐿−3 )(𝐿𝑡 −1 )2 = 𝑀𝐿−1 𝑡 −2
All equal ∴ eqn is homogenous Question 9 [𝑅] = [
(𝑀𝑛−1 )(𝐿𝑡 −1 )2 𝑀𝑢2 ]= 𝑇 𝑇
[𝑅] = [𝑀][𝑛]−1 [𝐿]2 [𝑡]−2 [𝑇]−1
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