Question

Proposes a dimensionless quantity that combines volume flow rate Q, density p viscosity u of the fluid, and depth h.

Answer 1

`(\rho*Q)/(\mu*h)`

Step-by-step explanation:

First, we need to establish the unit of each variable:

• 
  `Q (flow rate)=[m^3/s]`

• 
  `\rho(density)=[kg/m^3]`

• 
  `h(depth)=[m]`

• 
  `\mu( viscosity )=[kg/m*s]`

To eliminate
`m^3` we need to multiply Q by
`\rho`. Then to eliminate kg we divide
`\rho` by
`\mu`. Finally, multiply
`\mu` by h we can let the constant dimensionless.