Question

2. Internal Viscous Flow a) Pumps are used to circulate hot water through a home heating system. Summarize, in your own words, all the forces the pump must overcome to maintain a constant flow rate. Use the vector form of the Navier-Stokes equation to prove your answer. b) Apply the solution methods you learned to solve the following engineering problem: Water flows steadily through a smooth, circular, horizontal pipe. The discharge rate is 0.04 m/s and the pipe diameter is 0.15 m. Find the difference in pressure between two points 122 m apart if the water temperature is 15°C.

Answer 1

Solalions → Forces must be overcomed by pump. 1. Friction Force 2. polential Iman / weight of liquid Imales which is needed to pump. Navier -stroke qualion: po tus Bunt une au ta ) = Assumptions: → pipe is long in a direction > this is parallel flow allrao → flow is laminer & In compressible. > velocity field bis ar symmetric with no Swiral, nozo + Now above equation is reduced to 5 e com L op Scanned with CamScanner

p=f(x) ode = o ofta от 9 и да 82 dp tc, ens+C₂ ull de e at dp (0²_R²) - ell da 2T R uerdo de 020 720 CD (2² R2 rdr da ull = TRY & P da 8 el So, dx=L, dp AP AP = 80 Lee TRY bo Given values are = 0.04m3/ D = 0.15 Rn L-120m C Scanned with CamScanner

temperature at 150c, le = 1. 1375 x 103 pa.s. 80 L M Мои др - пRч Схо-04 X1 22 х 3 75 х ( ДР = 446 - 75 PG . Scanned with CamScanner