Question

After an initial test run John determines that his cooling system generates 45 W of heat loss. Calculate the amount of heat loss (H2), in W, that Mike expects his pump to do if its fan speed were 3.5 times greater and the coolant density was 9.5 times smaller.

Answer 1

Given:

heat generated by John's cooling system,  $H = \rho A v^{3}$  = 45 W    (1)

If ρ, A, and v corresponds to John's cooling system then let $\rho_{1}, A_{1}, v_{1}$ be the variables for Mike's system then:

$\rho = 9.5\rho_{1}$

$\rho_{1} = \frac{\rho}{9.5}$

$v_{1} =3.5 v$

Formula use:

Heat generated, $H = \rho A v^{3}$

where,

$\rho$ = density

A = area

v = velocity

Solution:

for Mike's cooling system:

$H_{2}$ = $v_{1}^{3}{1}A_{1}\rho_{1}$

⇒ $H_{2}$ = $(3.5v)^{3}$ × A × $\frac{\rho}{9.5}$

$H_{2}$ = 4.513$v^{3}$ A  $\rho$

Using eqn (1) in the above eqn, we get:

$H_{2}$ = 4.513 × 45 = 203.09 W