QUESTION $3[25]$

Water is being transferred from a lower reservoir to an upper reservoir level using a centrifugal pump as

motive force between difference in fluid surface elevations as shown in Figure $1.$ The characteristic of a

centrifugal pump handling water is given in Table $2.$

Table $2$: The characteristics of a centrifugal pump

The existing system consists of $840m$ of $15cm$ diameter pipes with absolutes roughness $6{10}^{-6}m$ joining

two reservoirs, the difference between water levels being $3m$ through a pipe with a friction factor of $0\mathrm{.}01.$

Neglecting all losses except frictions.

rigure $1$

As an engineer, you're responsible for specifying the final pipe sizes that will produce reasonably optimum

performance while considering system energy losses and pump power requirements. Therefore, it is

proposed to use pipe diameter as a control parameter to optimize the system and improve the pump's

operation at $80\%$ efficiency. In this case, the optimum efficiency is described as the optimization point.

i$.$ What is the volume flow rate and system head between two reservoirs?

ii$.$ What is the power consumed by the pump?

iii. What is the optimal diameter that would enable the pump to operate at the $80\%$ efficiency?

iv$.$ How does the optimised system will affect the volume flow rate, the system head and the power

consumed by the pump?QUESTION $3[25]$

Water is being transferred from a lower reservoir to an upper reservoir level using a centrifugal pump as

motive force between difference in fluid surface elevations as shown in Figure $1.$ The characteristic of a

centrifugal pump handling water is given in Table $2.$

Table $2$: The characteristics of a centrifugal pump

Q $($m$3$

$/$sec$)0\mathrm{.}010\mathrm{.}0140\mathrm{.}0170\mathrm{.}0190\mathrm{.}024$

H$($m$)9\mathrm{.}58\mathrm{.}77\mathrm{.}46\mathrm{.}10\mathrm{.}9$

Efficiency $(\%)6581786812$

The existing system consists of $840$ m of $15$ cm diameter pipes with absolutes roughness $6$x$10-6$ m joining

two reservoirs, the difference between water levels being $3$ m through a pipe with a friction factor of $0\mathrm{.}01.$

Neglecting all losses except frictions.

Figure $1$

As an engineer, you're responsible for specifying the final pipe sizes that will produce reasonably optimum

performance while considering system energy losses and pump power requirements. Therefore, it is

proposed to use pipe diameter as a control parameter to optimize the system and improve the pump's

operation at $80\%$ efficiency. In this case, the optimum efficiency is described as the optimization point.

i$.$ What is the volume flow rate and system head between two reservoirs?

ii$.$ What is the power consumed by the pump?

iii. What is the optimal diameter that would enable the pump to operate at the $80\%$ efficiency?

iv$.$ How does the optimised system will affect the volume flow rate, the system head and the power

consumed by the pump?

QUESTION $3[25]$

Water is being transferred from a lower reservoir to an upper reservoir level using a centrifugal pump as motive force between difference in fluid surface elevations as shown in Figure $1.$ The characteristic of a centrifugal pump handling water is given in Table $2.$

Table $2$: The characteristics of a centrifugal pump

$\backslash$table$[[Q(\frac{m^3}{sec}),0\mathrm{.}01,0\mathrm{.}014,0\mathrm{.}017,0\mathrm{.}019,0\mathrm{.}024],[H(m),9\mathrm{.}5,8\mathrm{.}7,7\mathrm{.}4,6\mathrm{.}1,0\mathrm{.}9],[$Efficiency $(\%),65,81,78,68,12]]$

The existing system consists of $840m$ of $15cm$ diameter pipes with absolutes roughness $6{10}^{-6}m$ joining two reservoirs, the difference between water levels being $3m$ through a pipe with a friction factor of $0\mathrm{.}01.$ Neglecting all losses except frictions.

Figure $1$

As an engineer, you're responsible for specifying the final pipe sizes that will produce reasonably optimum performance while considering system energy losses and pump power requirements. Therefore, it is proposed to use pipe diameter as a control parameter to optimize the system and improve the pump's operation at $80\%$ efficiency. In this case, the optimum efficiency is described as the optimization point.

i$.$ What is the volume flow rate and system head between two reservoirs?

ii$.$ What is the power consumed by the pump?

iii. What is the optimal diameter that would enable the pump to operate at the $80\%$ efficiency?

iv$.$ How does the optimised system will affect the volume flow rate, the system head and the power consumed by the pump?

$2$