Fluids Homework 2010
1.
High-heeled shoes can cause tremendous pressure to be applied to the floor. Suppose the radius
of a heel is 6.00 10-3 m. At times during a normal walking motion, nearly the entire body
weight acts perpendicular to the surface of such a heel. Find the pressure that is applied to the
floor under the heel because of the weight of a 60.0 kg woman.
Pa
2.
The main water line enters a house on the first floor. The line has a gauge pressure of 2.10 105
Pa.
(a) A faucet on the second floor, 5.4 m above the first floor, is turned off. What is the gauge
pressure at this faucet?
Pa
(b) How high above the water main could a faucet be before no water would flow from it, even if
the faucet were open?
m
3.
The drawing shows an intravenous feeding. With the distance shown, nutrient solution (ρ = 1050
kg/m3) can just barely enter the blood in the vein. What is the gauge pressure of the venous
blood? Express your answer in millimeters of mercury.
mm Hg
4.
The drawing shows a hydraulic chamber in which a spring (spring constant = 1559 N/m) is
attached to the input piston, and a rock of mass 36.2 kg rests on the output plunger. The piston
and plunger are at the same height, and each has a negligible mass. By how much is the spring
compressed from its unstrained position?
m
5.
Suppose that blood flows through the aorta with a speed of 0.44 m/s. The cross-sectional area of
the aorta is 1.0 10-4 m2.
(a) Find the volume flow rate of the blood.
m3/s
(b) The aorta branches into tens of thousands of capillaries whose total cross-sectional area is
about 1.92 m2. What is the average blood speed through them?
m/s
6.
The water tower in the drawing is drained by a pipe that extends to the ground. The flow is
nonviscous.
(a) What is the absolute pressure at point 1 if the valve is closed, assuming that the top surface of
the water at point 2 is at atmospheric pressure.
Pa
(b) What is the absolute pressure at point 1 when the valve is opened and the water is flowing?
Assume that the water speed at point 2 is negligible.
Pa
(c) Assuming the effective cross-sectional area of the valve opening is 1.65 10-2m2, find the
volume flow rate at point 1.
m3/s
7.
A venturi meter is a device for measuring the speed of a fluid within a pipe. The drawing shows
a gas flowing at a speed v2 through a horizontal section of pipe whose cross-sectional area A2 =
0.0600 m2. The gas has a density of ρ = 1.50 kg/m3. The Venturi meter has a cross-sectional area
of A1 = 0.0300 m2 and has been substituted for a section of the larger pipe. The pressure
difference between the sections is P2 - P1 = 140 Pa.
(a) Find the speed v2 of the gas in the larger original pipe.
m/s
(b) Find the volume flow rate Q of the gas.
m3/s
8.
A water tower is a familiar sight in many towns. The purpose of such a tower is to provide
storage capacity and to provide sufficient pressure in the pipes that deliver the water to
customers. The drawing shows a spherical reservoir that contains 5.75 105 kg of water when
full. (h = 7.20 m.) The reservoir is vented to the atmosphere at the top. For a full reservoir, find
the gauge pressure that the water has at the faucet in each house.
(a) house A
Pa
(b) house B
Pa
9.
Find the pressure increase in the fluid in a syringe when a nurse applies a force of 41 N to the
syringe's circular piston, which has a radius of 1.1 cm.
Pa
10.
Calculate the hydrostatic difference in blood pressure between the brain and the foot in a person
of height 1.63 m. The density of blood is 1.06 103 kg/m3.
Pa
11.
A boat floating in fresh water displaces water weighing 32.4 kN.
(a) What is the weight of the water that this boat would displace if it were floating in salt water
with a density of 1.10 103 kg/m3?
kN
(b) Would the volume of displaced water change?
Yes, it would increase.
No, it would stay the same.
Yes, it would decrease.
If so, by how much?
m3
12.
In Fig. 15-35, a cubical object of dimensions L = 0.630 m on a side and with a mass of 540 kg is
suspended by a rope in an open tank of liquid of density 1030 kg/m3.
(a) Find the magnitude of the total downward force on the top of the object from the liquid and
the atmosphere, assuming that atmospheric pressure is 1.00 atm.
N
(b) Find the magnitude of the total upward force on the bottom of the object.
N
(c) Find the tension in the rope.
N
(d) Calculate the magnitude of the buoyant force on the object using Archimedes' principle.
N
What relation exists among all these quantities?
13.
A block of wood floats in water with one third of its volume submerged. In oil the block floats
with 0.45 of its volume submerged.
(a) Find the density of the wood.
g/cm3
(b) Find the density of the oil.
g/cm3
14.
Water is moving with a speed of 4.9 m/s through a pipe with a cross-sectional area of 3.7 cm2.
The water gradually descends 7 m as the pipe increases in area to 7.7 cm2.
(a) What is the speed at the lower level?
m/s
(b) If the pressure at the upper level is 1.5 105 Pa, what is the pressure at the lower level?
Pa
15.
A water intake at a pump storage reservoir (Fig. 15-39) has a cross-sectional area of 0.71 m2. The
water flows in at a speed of 0.46 m/s. At the generator building 180 m below the intake point, the
cross-sectional area is smaller than at the intake and the water flows out at 9.1 m/s. What is the
difference in pressure, in megapascals, between inlet and outlet?
MPa
16.
In Fig. 15-40, water flows through a horizontal pipe, and then out into the atmosphere at a speed
of 15 m/s. The diameters of the left and right sections of the pipe are 5.4 cm and 2.8 cm,
respectively.
(a) What volume of water flows into the atmosphere during a 15 min period?
m3
(b) What is the flow speed of the water in the left section of the pipe?
m/s
(c) What is the gauge pressure in the left section of the pipe?
Pa
17.
When a load of 1.0 106 N is placed on a battleship, the ship sinks only 2.3 cm in the ocean
water. Estimate the cross-sectional area of the ship at water level. (The density of ocean water is
1.025 103 kg/m3.)
m2
18.
A raft is constructed of wood having a density of 600.0 kg/m3. Its surface area is 6.5 m2, and its
volume is 0.56 m3. When the raft is placed in fresh water having a density of 1.0 103 kg/m3,
how much of it is below water level?
m
19.
A sample of an unknown material weighs 293.0 N in air and 198.4 N when submerged in an
alcohol solution with a density of 0.70 103 kg/m3. What is the density of the material?
kg/m3
20.
A submarine is at an ocean depth of 2.75 km.
(a) Calculate the absolute pressure at this depth. Assume that the density of water is 1.025 103
kg/m3 and that atmospheric pressure is 1.01 105 Pa.
Pa
(b) Calculate the total force exerted at this depth on a circular submarine window with a diameter
of 35.0 cm.
N
21.
The hypodermic syringe shown in Figure 9-19 contains a medicine with the same density as
water. The barrel of the syringe has a cross-sectional area of 2.25 10-5 m2. The cross-sectional
area of the needle is 1.00 10-8 m2. In the absence of a force on the plunger, the pressure
everywhere is 1.00 atm. A 2.10 N force is exerted on the plunger, making medicine squirt from
the needle. Determine the speed of the emerging fluid. Assume that the pressure in the needle
remains at 1.00 atm, that the syringe is horizontal, and that the speed of the emerging fluid is the
same as the speed of the fluid in the needle.
m/s