Question

NO QUESTIONS DURING T Water is to be pumped from a reservoir (ZA30 /s- to another reservoir at a higher elevati rate of elevation (Zn THE EXAM! n) through a long pipe, as shown in the figure at a volume ow olume flow rate has been calculated and is 11 m he head loss in the pipe at this usefuf pump ) Demostrate that wh en a pump moves a fluid from one reservoir to ano e elevation difference between the two reservoirs plus reservoir to another, the usefuf pump head require is equal to th Neglecting the minor losses determine ) the useful pumping power. e the pressure difference between the inlet C and the exit D of the pump. l) If the rake the density of water ρ = 1000 kg/m" and the acceleration of gravity g Hint: Wpump.u is the electric power drawn during operation? = 9.81 m/s. r-pump combination has an efficiency of 70% what is the electric ZB = 13 m Pump

Answer 1

From bernoulli's theorem we know that
P/rho*g is the pressure head of flowing fluid and h ( height from the reference) is its potential head

i. for the given problem
   when the pump moves fluid from one reservoir to the another one
   useful head requirement = hpump,u
   now head shall be used by the pump for the following two purposes
   a. covering the potential head h = zb - za
   b. some loss of pressure in the form of pressure head ( the pressure of the fluid shall nor remain constant throughout the flow) = hl
   hence
   hpump,u = (zb - za) + hl

ii. given, volume flow rate, r' = 30 L/s = 30*10^-3 m^3/s
   h = zb - za = 8 m
   also, hl = 11m ( given)
   hence
   hpump,u = 11 + 8 = 19 m
   useful pumping power = hpump,u*g*rho*r'
   rho = 1000 kg/m^3
   P = 3237.3 W

iii. Pc - Pd = ?
   now, from bernoullis theorem

   Pc - Pd = rho*g*hl = 107910 Pa

iv. given efficiency, n = 0.7
   power drawn = P/n = 4624.714285 W