Machinery's Handbook, 31st Edition
ESTIMATING EFFICIENCY 2809 size between pumps grows. Note that as the specific speed increases, the accuracy of the affinity equations decreases. To estimate the efficiency of a very different size pump, the following equation can be used. S – 1 η L – = -------- where subscript L denotes the larger pump, and S denotes the smaller pump. D is impeller diameter and n is speed. The affinity equations (assuming equal efficiencies) which allow comparison between pumps are as follows: • When the impeller diameter is constant while the speed changes: D L D S ---- n 1 η
n 2 n 1 --- 2
Q 2 Q 1 --- 2
n 2 n 1 --- 3
Q 2 Q 1 --- 3
n 2 n 1 ---
Q 2 Q 1 = ---
h 2 h 1 ---
P 2 P 1 ---
= =
= =
• When the speed is constant and the impeller size changes: D 2 D 1 --- Q 2 Q 1 = --- D 2 D 1 --- 2 h 2 h 1 = --- D 2 D 1 --- 3
P
2 P 1 = --- • When flow is assumed to be turbulent and the percentage of wide open flow is assumed to be the same, similarity can be used as follows:
ρ 2 ρ 1 ---
n 2 n 1 --- 2 D
n 2 n 1 --- 3 D
n 2 n 1 ---
D 2 D 1 --- 3
2 D 1 --- 2
2 D 1 --- 5
Q 2 Q 1 ---
h 2 h 1 ---
P 2 P 1 ---
=
=
=
Startup Conditions: Priming is necessary for all types of pumps to begin operation. During priming, the inlet chamber is flooded with fluid, and gas is purged from the pump mechanism. Submersible pumps are generally self-priming, as are some types of non- submersible pumps. The torque requirements of centrifugal pumps at startup are greatly different from run ning torque requirements. Full-load torque is required for starting against full discharge pressure. To reduce the startup torque required, the designer can pipe the discharge back to the suction line, and close it off from any head inherent in the running discharge line. This equalizes discharge and suction pressure and eliminates the load on the pump during startup. Using valves, this loop can be closed off and the pump discharge connected to the discharge pipe system once the pump gets up to running speed. Piping Considerations: To ensure peak performance of hydraulic systems, some points to consider are: • Make piping runs as short and direct as possible. • Design for minimum fluid velocities and accelerations. • Use long radius bends rather than elbows to redirect piping where possible. • Design pipe systems to preclude the collection of vapor bubbles, except where venting is provided. • Include pulsation dampeners and suction stabilizers where acceleration head is high or the fluid needs degassing. A suction stabilizer is a device placed on the suction line of a pump that both absorbs pulsations and separates free gases from the liquid being pumped. • Always ensure that NPSHA >> NPSHR . • Include strainers only when absolutely necessary, and ensure regular maintenance is conducted. • Provide a relief valve that is adequately sized. • Pipe a bypass line around the pump with valves so that the pump may be started with low load. This must be done slowly to avoid shock to the system. • In systems with high static discharge heads, install a check valve at the pump discharge to prevent static pressure from loading the pump during startup.
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