The power gained by fluid from operating pumps or fans

[h=3]Power Gained by Fluid[/h] The power gained by the fluid from a pump or fan can be expressed as:
[INDENT] [I]P = m w[/I][I] (1)[/I]
[I]where[/I]
[I]P[/I][I] = power[/I]
[I]m[/I][I] = mass flow rate[/I]
[I]w[/I][I] = specific work[/I]
[/INDENT][h=3]Specific Work[/h] Specific work - [I]w[/I] - can be expressed:
[INDENT] [I]w = g h[/I][I] (2)[/I]
[I]where[/I]
[I]h[/I][I] = head[/I]

[I]g[/I][I] = acceleration of gravity[/I]
[/INDENT][h=3]Mass Flow Rate[/h] Mass flow rate - [I]m -[/I] can be expressed:
[INDENT] [I]m =[/I] [I]ρ Q[/I][I] (3)[/I]
[I]where[/I]
[I]ρ[/I][I] = density[/I]

[I]Q[/I][I] = volume flow rate[/I][/INDENT]Combining (1), (2) and (3) the power gained by the fluid from a pump or fan can be expressed as:
[INDENT] [I]P = ρ Q g h[/I][I] (4)[/I][/INDENT]With specific weight expressed as:
[INDENT] [I]γ[/I][I] = [/I] [I]ρ g[/I][I] (5)[/I]
[I]where[/I]
[I]γ[/I] [I]=[/I][I] specific weight[/I]
[/INDENT]equation (4) can be modified so the power gained by the fluid from a pump or fan can be expressed as:
[INDENT] [I]P = γ Q h[/I][I] (6)[/I][/INDENT]Since head can be expressed as

[INDENT] [I]h = (p[SUB]2[/SUB] - p[SUB]1[/SUB]) /[/I] [I]γ[/I][I] (7)[/I][/INDENT]equation (4) can be modified so the power gained by the fluid from a pump or fan can be expressed as:
[INDENT] [I]P = Q (p[SUB]2[/SUB] - p[SUB]1[/SUB])[/I][I] (8)[/I][/INDENT][h=4]Example - Head Rise of a Inline Pump[/h] An inline water pump works between measured pressure [I]1 bar (1 10[SUP]5[/SUP] N/m[SUP]2[/SUP])[/I] and [I]10 bar (10 10[SUP]5[/SUP] N/m[SUP]2[/SUP])[/I]. Density of water is [I]1,000 kg/m[SUP]3[/SUP][/I]. The volume flow is measured to [I]1 10[SUP]-3[/SUP] m[SUP]3[/SUP]/s[/I].

The actual water head (water column) can be calculated using (7):
[INDENT] [I]h = (p[SUB]2[/SUB] - p[SUB]1[/SUB]) /[/I] [I]γ[/I]
[I] = (p[SUB]2[/SUB] - p[SUB]1[/SUB]) /[/I] [I]ρ g[/I]
[I] =[/I][I] ((10 10[SUP]5[/SUP] N/m[SUP]2[/SUP]) - (1 10[SUP]5[/SUP] N/m[SUP]2[/SUP])) / (1,000 kg/m[SUP]3[/SUP]) (9.81 m/s[SUP]2[/SUP])[/I]
[I] = [U]91.7[/U] m - water column[/I][/INDENT]The power gained by the fluid can be calculated using equation (4):
[INDENT] [I]P = ρ Q g h[/I]
[I] = (1,000 kg/m[SUP]3[/SUP]) (1 10[SUP]-3[/SUP] m[SUP]3[/SUP]/s) (9.81 m/s[SUP]2[/SUP]) (91.7 m)[/I]
[I] = [U]899.6[/U] kg.m[SUP]2[/SUP]/s[SUP]3[/SUP] (W) [/I]
[I] = [U]0.9[/U] kW[/I]
[/INDENT]