Question

Dimensional formula for pressure head is

Answer 1

What is the dimensional formula of a pressure head?

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2 ANSWERS



Shiv Shankar Nandi, Bsc Chemistry & Cosmology, Colleges and Universities (2017)

Answered May 27

Pressure is defined is force/area

Lets analyse the dimensions of the two parameters

Force= mass ×acceration

= [L MT^-2] ••••••••••••••(1)

Area=meter square

=[L^2]. •••••••••••••(2)

Dividing 1 and 2,

[LMT^-2]/[L^2]

= [L^-1M T^-2]

The above is dimensions of pressure,now considering unit,

Dividing not numerator and denominator by [L^2] we get,

[LMT^-2]/[L^2]

Thus unit is Newton per meters square

Answer 2

since pressure =force/area
since force =mass×acceleration
=
$m1 l1t - 2$
Area=L
$l ^{2}$
now dimensional formula of pressure=dimensional formula of force÷dimensional firmula of area.


i.e.
$m 1 \: l1t ^{ - 2} \div l {}^{2} = m ^{1} l ^{ - 1} t ^{ - 2}$

now,since pressure head=Pressure÷density ×g

$dimensions \:of \:pressure \: head = dimensions \: of \: pressure \div dimensions \: of \: density \times dimensions \: of \: g$

➡
$m ^{1} l ^{ - 1} t ^{ - 2} \div m ^{1} \div l ^{3} \times l ^{1} t ^{ - 2} = m ^{0} l ^{1} t ^{0}$
thus dimensional formula of pressure head=
$m ^{0} l ^{1} t ^{0}$

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