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Inessa [10]
3 years ago
9

A water pump delivers 6 hp of shaft power when operating. The pressure differential between the outlet and the inlet of the pump

is measured to be 1.2 psi when the flow rate is 10 ft3/s, and the velocity changes to 5 ft/s from 2 ft/s as the water passes through the pump. Determine the mechanical efficiency of this pump assuming the water density to be 62.4 lbm/ft3 (written in decimal form with 3 significant figures).
Engineering
1 answer:
frez [133]3 years ago
5 0

Answer: Pump efficiency = 0.585 = 58.5%

Explanation: Pump efficiency = (power gained by the fluid)/(power supplied by the shaft)

Power gained by the fluid = Q(ΔP) + m(((v2)^2) - ((v1)^2))/2

Where Q = volumetric flow rate = 10 ft3/s = 0.283 m3/s

ΔP = 1.2 psia = 8273.709 Pa

m = mass flow rate = density × volumetric flow rate

Density = 62.4 lbm/ft3 = 999.52 kg/m3

m = 999.52 × 0.283 = 282.86 kg/s

v2 = 5ft/s = 1.524 m/s

v1 = 2ft/s = 0.61 m/s

Q(ΔP) = 0.283 × 8273.709 = 2341.46 W

Power from change in kinetic energy = m(((v2)^2) - ((v1)^2))/2 = 275.92 W

Power gained by the fluid = 2341.46 + 275.92 = 2617.38 W

Power supplied by shaft = 6hp = 6 × 746 = 4476 W

Efficiency = 2617.38/4476 = 0.58475 = 0.585 to 3s.f

QED!

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3 years ago
A heat engine receives heat from a heat source at 1453 C and has a thermal efficiency of 43 percent. The heat engine does maximu
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Answer:

a) 1253 kJ

b) 714 kJ

c) 946 C

Explanation:

The thermal efficiency is given by this equation

η = L/Q1

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Rearranging:

Q1 = L/η

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The first law of thermodynamics states that:

Q = L + ΔU

For a machine working in cycles ΔU is zero between homologous parts of the cycle.

Also we must remember that we count heat entering the system as positiv and heat leaving as negative.

We split the heat on the part that enters and the part that leaves.

Q1 + Q2 = L + 0

Q2 = L - Q1

Q2 = 539 - 1253 = -714 kJ

TO calculate a temperature for the heat sink we must consider this cycle as a Carnot cycle. Then we can use the thermal efficiency equation for the Carnot cycle, this one uses temperatures:

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3 years ago
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