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If the Bernoulli's equation may be written as P + 1/2 p v^2 + hpg = k (constant) where P is pressure, p is density, v is velocity and h is height, find out unit and dimensional formula for k/pv^2.

If the Bernoulli's equation may be written as P + 1/2 p v^2 + hpg = k (constant) where P is pressure, p is density, v is velocity and h is height, find out unit and dimensional formula for k/pv^2.

Grade:11

4 Answers

Ramesh V
70 Points
12 years ago

the constant k(total head) has dimensions of pressure head i.e., N/m2 with dim. formula ML-1T-2

 

so unit and dimensional formula for k/pv^2 is Dimensionless(no units) and formula is M0L0T0

 
AskIITianExpert Srijan.iitd
8 Points
12 years ago

pv^2 is having the same dimention as the constant k  because we kno that for two physical terms to be summable they should have same dimentions,hence all terms on left hand side have same dimentions.Also dimention of left hand side of any physical equation must have same dimention as the right hand side ,hence constant k have same dimentions as the terms "P", P v^2 and hpg.

hence the term k/pv^2 is dimentionless!!!=> M^0L^0T^0.

AskiitianExpert Shine
10 Points
12 years ago

Hi

For the statement to be dimensionally correct, every term should have the same units. This means P, (pv^2)/2 , hpg and k should all have same units.
Hence, the term k/(pv^2) should be dimensionless.

LISA
14 Points
one month ago
K=p+hpg+1/2pv²
[K]=[p]+[h][p][g]+1/2[p][v]²
[K]=[ML-1T-2+[M°L¹T°][M¹L-3T°][M°L²T-2]+           [ML-3T°][M°L¹T-1]
[K]=[M¹L-1T-2]
 

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