Question

A pump increases the water pressure from 100 kPa at the inlet to 900 kPa at the outlet. Water enters this pump at 15 °C through a 1 cm diameter opening and exist through a 1.5 cm diameter opening. Determine the velocity of the water at the inlet and the outlet when the mass flow rate through the pump is 0.5 kg/s. Will these velocities change significantly if the inlet temperature is raised to 40 °C? (prove it by an appropriate calculation)​

Answer 1

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Answer 2

Given:

Water pressure at the inlet: 100 kPa

Water pressure at the outlet: 900 kPa

Water temperature at the inlet: 15°C

Inlet diameter: 1 cm

Outlet diameter: 1.5 cm

Mass flow rate: 0.5 kg/s.

To find: The velocity of water at the inlet and outlet and to determine if the velocities will change significantly if the inlet temperature is raised to 40°C.

Solution:

Using the equation of continuity: A1v1 = A2v2, where A1 and A2 are the cross-sectional areas of the inlet and outlet, respectively, and v1 and v2 are the velocities at the inlet and outlet, respectively.

• The area of the inlet, A1, is calculated as: A1 = π(0.01 m)^2 / 4 = 7.85 x 10^-5 m^2
• The area of the outlet, A2, is calculated as: A2 = π(0.015 m)^2 / 4 = 1.77 x 10^-4 m^2
• Substituting the given mass flow rate of 0.5 kg/s and the density of water at 15°C, which is approximately 999 kg/m^3, we can solve for v1: v1 = (A2/A1) * (0.5 kg/s) / ρ = 1.13 m/s.

Using Bernoulli's equation: P1 + (1/2)ρv1^2 = P2 + (1/2)ρv2^2, where P1 and P2 are the pressures at the inlet and outlet, respectively, and v2 is the velocity at the outlet.

• Substituting the given pressures and the calculated velocity at the inlet, we can solve for v2: v2 = √[2(P1 - P2) / ρ + v1^2] = 11.7 m/s.
• To check if the velocities will change significantly if the inlet temperature is raised to 40°C, we can recalculate the density of water at that temperature and use it in the above equations.

Using a table, we find that the density of water at 40°C is approximately 992 kg/m^3.

• Substituting this value into the above equations, we find that the velocity at the inlet increases slightly to 1.14 m/s, and the velocity at the outlet increases to 12.2 m/s.
• These changes are relatively small and can be considered insignificant.

Therefore, the velocity of water at the inlet is 1.13 m/s, and at the outlet, it is 11.7 m/s. The velocities will change slightly if the inlet temperature is raised to 40°C, but the changes can be considered insignificant.

To learn more about velocity from the given link.

https://brainly.in/question/36267867

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