If V=volume, p=specific weight and Q=flow rate, determine the dimensional equation for K=VpQ



Answer to a math question If V=volume, p=specific weight and Q=flow rate, determine the dimensional equation for K=VpQ

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Para determinar la ecuación dimensional para K = VpQ , vamos a analizar las dimensiones de cada una de las variables involucradas:

- El volumen ( V ) se mide en metros cúbicos ( m^3 ).
- El peso específico ( p ) se mide en Newtons por metro cúbico ( N/m^3 ).
- El caudal ( Q ) se mide en metros cúbicos por segundo ( m^3/s ).

Ahora, vamos a expresar las dimensiones de cada variable en términos de sus unidades fundamentales de longitud ( L ), masa ( M ), y tiempo ( T ):

- Volumen: [V] = L^3
- Peso específico: [p] = \frac{F}{V} = \frac{MLT^{-2}}{L^3} = ML^{-2}T^{-2}
- Caudal: [Q]=\frac{V}{T}=\frac{L^3}{T}=L^3T^{-1}

Sustituimos las dimensiones de cada variable en la expresión para K = VpQ :

[K]=[V]\cdot[p]\cdot[Q]=L^3\cdot ML^{-2}T^{-2}\cdot L^3T^{-1}=ML^4T^{-3}

Por lo tanto, la ecuación dimensional para K = VpQ es:


\textbf{Respuesta:} La ecuación dimensional para K = VpQ es K=ML^4T^{-3} .

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