Question 1

The pressure, above atmosphere, required to send water a vertical height of 25 m is

Accepted Answer

The pressure required to lift water to a height of 25 m can be calculated using the formula P = hρg, where h is the height (25 m), ρ is the density of water (approximately 1000 kg/m³), and g is the acceleration due to gravity (approximately 9.81 m/s²). This gives a pressure of about 245,250 Pa, which is approximately 2.4 atmospheres when converted (1 atmosphere ≈ 101,325 Pa).

Question 2

A large water tower has a small hole that is 1.5 m below the surface. The initial speed of the water leaving the hole is

Accepted Answer

The answer of A large water tower has a small...

Question 3

The radius of a pipe is doubled. The velocity of the fluid inside the pipe will

Accepted Answer

According to the continuity equation, the product of the cross-sectional area of a pipe and the velocity of the fluid flowing through it remains constant (A1V1 = A2V2). When the radius is doubled, the area (πr^2) increases by a factor of 4. To maintain the same flow rate, the velocity must decrease by a factor of 4.

Question 4

An incompressible fluid flows through a pipe. The radius of the pipe at point A is twice as large as the radius at point B. The pressure of the fluid at point B is

Accepted Answer

According to the principle of conservation of mass and Bernoulli's equation, the velocity of the fluid increases as it moves from a wider section (point A) to a narrower section (point B). An increase in velocity results in a decrease in pressure at point B compared to point A.

Question 5

An incompressible fluid flows through a pipe. The radius of the pipe at point A is twice as large as the radius at point B. The velocity of the fluid at point B is

Accepted Answer

The velocity of the fluid at point B is greater than at point A due to the principle of continuity for incompressible fluids, which states that the product of the cross-sectional area and the velocity of the fluid must remain constant throughout its flow. Since the radius at point A is twice as large, its area is four times larger, necessitating a higher velocity at point B to maintain constant flow.

Question 6

An incompressible fluid (density of 920 kg/m³) flows at 10.0 m/s through a level pipe with a cross-sectional area of 1.5 cm². The pressure of the fluid in this section of the pipe is 150 kPa. The pipe is connected to a second pipe whose cross-sectional area is 2.5 cm². The speed of the flow in the second pipe is

Accepted Answer

According to the principle of continuity for incompressible fluids, the flow rate must remain constant. Therefore, A1 * V1 = A2 * V2. Solving for V2 gives (1.5 cm² * 10.0 m/s) / 2.5 cm² = 6.0 m/s.

Question 7

An incompressible fluid, whose density is 1000 kg/m³, flows at 4.5 m/s through a horizontal pipe with a radius of 1.0 cm. The pressure in the fluid is 115 kPa. The pipe is connected to a second pipe with a radius of 1.5 cm. The speed of the flow in the second pipe is

Accepted Answer

The flow rate must be conserved in an incompressible fluid. The flow rate is given by the product of the cross-sectional area and the velocity. The area of the first pipe is π(0.01 m)^2 and the velocity is 4.5 m/s. The area of the second pipe is π(0.015 m)^2. Setting the flow rates equal gives: π(0.01 m)^2 * 4.5 m/s = π(0.015 m)^2 * v. Solving for v gives v = 2.0 m/s.

Question 8

An incompressible fluid is moving at 12 m/s through a pipe that has a radius of 1.25 cm. The pipe descends a distance of 4.0 m. To maintain the same pressure at each section of the pipe, the velocity of the fluid in the lower region is

Accepted Answer

The answer of An incompressible fluid is moving at 12...

Question 9

An incompressible fluid moves at 12 m/s through a pipe that has a radius of 1.25 cm. The pipe descends a distance of 4.0 m. To maintain the same pressure at each end of the pipe, the radius of the pipe in the lower region is

Accepted Answer

The answer of An incompressible fluid moves at 12 m/s...

Question 10

The face of a dam can be considered a vertical rectangle of height 20 m and width of 50 m. Find the total fluid force exerted on the dam by the water when the water surface level is near the top of the dam:

Accepted Answer

The total fluid force exerted on the dam can be calculated using the formula: Force = ρghA, where ρ is the density of water (1000 kg/m^3), g is the acceleration due to gravity (9.8 m/s^2), h is the depth of the water (which, in this case, can be taken as the average depth of 10 m, since the pressure varies linearly with depth), and A is the area of the dam face (20 m * 50 m = 1000 m^2). Plugging in these values gives a force of 9.8 * 10^7 N, which matches choice D.

Quiz 18: Fluid Mechanics