1. A garden hose of diameter 2 cm is used to fill a 20 liter bucket. If it takes 1 minute to fill the bucket, what is the speed at which water enters the hose?
a) 106.1 cm/s
b) 106 cm/s
c) 106.5 cm/s
d) 106.8 cm/s
Explanation: The cross-sectional area of the hose will be given by:
A1 = π r2 = π (2 cm/2)2 = π cm2
To find the velocity, v1, we use
Flow rate = A1 v1 = 20.0 L/min = \(\frac{20.0 × 10^3 cm^3}{60.0 s}\)
v1 = \(\frac{20.0 × \frac{10^3 cm^3}{60.0s}}{\pi cm^2}\)
= 106.1 cm/s
2. Refer to Q1 and estimate a practical joker pinches the open end of the hose down to a diameter of 5 mm, and sprays his neighbor with it. What is the speed at which water comes out of the hose?
a) 1690 cm/s
b) 1660 cm/s
c) 1698 cm/s
d) 1668 cm/s
Explanation: The flow rate (A1v1) of the water approaching the constriction must be equal to the flow rate leaving the hose (A2v2). This gives:
v2 = \(\frac{A_1 v_1}{A_2}\)
= \(\frac{(\pi)(106.1)}{(\pi)(0.5/2)^2}\)
= 1698 cm/s.
3. Water flows through a rubber hose 2 cm in diameter at a velocity of 4 m/s. What must be the diameter of the nozzle in order that the water emerge at 16 m/s?
a) 0.884 cm
b) 0.891 cm
c) 0.881 cm
d) 0.894 cm
Explanation: The area is proportional to the square of diameter, so:
v1d12 = v2d22
d22 = v1d12 / v2 = \(\frac{(4 \frac{m}{s})(2cm)^2}{(20 cm)^2}\)
d2 = 0.894 cm
4. Water flows through a rubber hose 2 cm in diameter at a velocity of 4 m/s. What is the rate of flow rate of flow in m3/min?
a) 0.0754 m3/min
b) 0.0750 m3/min
c) 0.0764 m3/min
d) 0.0760 m3/min
Explanation: R = v1A1 = v2A2
R = v1A1; A1 = \(\frac{\pi d_2^1}{4}\)
R1 = v1 \(\frac{\pi d_2^1}{4} = \frac{(4 \frac{m}{s})\pi(0.02 m)^2}{4}\)
R1 = 0.00126 m3/s
R1 = \(0.00126 \frac{m^3}{min} (\frac{1 min}{60 s})\)
R1 = 0.0754 m3/min.
5. Water ideally flows through a pipe of radius 6 centimeters at a rate of 5 meters per second. The pipe then narrows to a radius of 2 centimeters. What is the new velocity of the water?
a) 50 m/s
b) 55 m/s
c) 60 m/s
d) 65 m/s
Explanation: First convert everything to basic metric units.
(6cm)((1m)/(100cm)) = .06m
(2cm)((1m)/(100cm)) = .02m
Now find the cross-sectional area in both sections of the pipe.
A = π(r)2
π(.06)2 ≈ 0.011m2
π(.02)2 ≈ 0.001m2
Next, use the equation of continuity with the areas you have obtained and the given velocity.
A1v1 = A2v2
(0.011m2)(5m/s) = (.001m2)v2
0.055m3/s = (.001m2)v2
55m/s = v2.
6. Venturi relation is one of the applications of ___________
a) Light equation
b) Bernoulli’s equation
c) Speed equation
d) Equation of continuity
Explanation: The flow speed of a fluid can be measured using a device such as a Venturi meter or an orifice plate, which can be placed into a pipeline to reduce the diameter of the flow. For a horizontal device, the continuity equation shows that for an incompressible fluid, the reduction in diameter will cause an increase in the fluid flow speed. Subsequently, Bernoulli’s principle then shows that there must be a decrease in the pressure in the reduced diameter region. This phenomenon is known as the Venturi effect.
7. Simplified equation of continuity is represented as _____________
a) A1V2 = A2V2
b) A1V1 = A1V2
c) A2V1 = A1V1
d) A1V1 = A2V2
Explanation: Continuity uses the conservation of matter to describe the relationship between the velocities of a fluid in different sections of a system. The simple observation that the volume flow rate, Av, must be the same throughout a system provides a relationship between the velocity of the fluid through a pipe and the cross-sectional area. Continuity works in tandem with Bernoulli’s principle in the design and construction of systems of irrigation, plumbing, etc
8. Relative density of mercury is _____________
a) 13.6
b) 1
c) 1000
d) 9.8
Explanation: Relative density of a substance is the ratio of its density to that of water.ie. So relative density of mercury is 13.6 means that density of mercury is 13.6 times the density of water.
9. The unit of pressure one bar is ___________
a) 1 Pascal
b) 1 kilo Pascal
c) 100 kPascal
d) 1000 kPascal
Explanation: A bar (b) is a metric measurement unit of pressure. One bar is equivalent to ten newtons (N) per square centimeter (cm2).
1 bar = 100,000 Pascal = 100,000 N/m2 = 100,000 N / (100*100cm2) = 10 N/cm2.
10. Reynolds number signifies the ratio of ____________
a) inertia forces to gravity forces
b) buoyant forces to inertia forces
c) inertial forces to viscous forces
d) gravity forces top viscous forces
Explanation: The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities, in which is known as a boundary layer in the case of a bounding surface such as the interior of a pipe.