contestada

The flow rate of a Newtonian fluid is found to be proportional to the square root of the supply pressure. By what percentage must the supply pressure be increased to increase the flow rate of a Newtonian fluid by 25%

Respuesta :

opudodennis

Answer:

56.25%

Explanation:

Since flow rate of a Newtonian fluid is found to be proportional to the square root of the supply pressure then [tex]Q=k\sqrt {P}[/tex] where P is pressure and Q is flow rate and k is a constant of proportionality. Ignoring k

[tex]P=Q^{2}[/tex]

Now let pressure 1 be [tex]P_1=Q_1^{2}[\tex] then when flow rate is increased by 25% to mean 1.25 then [tex]P_2=(1.25Q_1)^{2}=1.5625Q_1^{2}[/tex] then the differences in these two pressures expressed as a percentage will be [tex]\frac{1.5625Q_1^{2}-Q_1^{2}}{Q_1^{2}}\times 100=56.25[/tex]