For a certain rocket the speed vb by which the solid propell

For a certain rocket the speed v_b by which the solid propellant bums is the following function of the pressure, p: v_b = alpha p^n where n is a non-dimensional constant. What are the SI units of the constant alpha ?

Solution

Here ,

as vb is velocity

unit of vb is m/s

p is pressure ,

unit of pressure is Pa = N/m^2

putting in the equation

m/s = alpha * N/m^2

alpha = m^3/(N*s)

the SI unit of alpha is m^3/(N*s)